This exam consists of 6 pages and 16 problems. Be sure you have all 6 pages before you start.

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "This exam consists of 6 pages and 16 problems. Be sure you have all 6 pages before you start."

Transcription

1 Math M119 Practice Test 1 PRINT your name This exam consists of 6 pages and 16 problems. Be sure you have all 6 pages before you start. Time: 75 minutes Scrap paper, notes, books, portable electronic devices, and laptops are not to be used during the exam. Cell phones should be off and put away. Earpieces other than medically required hearing aids are not permitted. The only permitted calculator is the TI30Xa. To receive credit, show supporting work. For money answers, give your answers to the nearest cent. For other decimals, give at least 3 decimal places in your answers. Do Not Write in this Area Pg 2 10 Pg 3 10 Pg 4 10 Pg 5 10 Pg 6 10 TOTAL 50 Math M119 Practice Test 1 page 1

2 1. Find a formula which expresses q as a linear function of p. p q q = (2) 2. A company is making lamps that sell for a suggested retail price of $129. The payroll and other fixed costs are $8,200 while the variable cost per unit is $55. a. Find and simplify the Profit function, π(q). Be sure to simplify and combine like terms. π(q) = (2) b. Find the number of units the company needs to sell in order to break even. Round your answer to the nearest whole number. (2) c. How many units does the company need to sell in order to make a profit of $30,000? Round your answer to the nearest whole number. (2) 3. What annual interest rate do you need if you want to double your money in 13 years? Assume that interest is compounded annually NOT continuously. Give 3 decimal places in your answer. % (2) Math M119 Practice Test 1 page 2

3 4. You want to accumulate $80,000 in 20 years. How much should you invest now if interest is compounded continuously at 4.25% per year? $ (2) 5. The table below gives values of a function w = f(t). t w a. Is the function increasing or decreasing? (1) b. Is the function concave up, concave down or neither? (1) c. Find the average rate of change of w between t = 0 and t = 4. (1) 6. Answer the questions about the function below: x g(x) a. Find a formula for the function. g(x) = (2) b. Is the function linear, exponential, or neither? (1) c. Is the function concave up, concave down, or neither? (1) d. Find the relative rate of change of g(x) between x = 1 and x = 3. % (1) Math M119 Practice Test 1 page 3

4 7. Answer the questions about the function below: x f(x) a. Is the function linear, exponential, or neither? (1) b. Is the function concave up, concave down, or neither? (1) c. Find a formula for the function. f(x) = (2) d. Find the average rate of change of f(x) between x = 1 and x = 7 (1) 8. When the price, p, charged for a latte was $4.75, the average number of lattes sold per week, N, was 200. When the price was reduced to $4.50, the average number of lattes sold per week increased to 230. Find a formula for the demand function, assuming that it is linear. N = (3) 9. You have $1200 to invest and your goal is for your deposit to grow to $2,000 in 10 years. What continuous annual interest rate do you need? Assume that interest is compounded continuously. Give your answer as a percent with at least 3 decimal places. % (2) Math M119 Practice Test 1 page 4

5 10. What continuous annual interest rate is equivalent to an annual interest rate of 5%? Give your answer as a percent with at least 3 decimal places. % (2) 11. What annual interest rate is equivalent to a continuous annual interest rate of 6.9%? Give your answer as a percent with at least 3 decimal places. % (2) 12. A car costs $23,000 today, and the price is reduced at the end of each day. How long will it take until the price drops below $17,000 for each scenario below? Include units in your answers. a. the price is reduced by 4% per day (this is NOT a continuous rate) (2) b. the price is reduced by $110 per day (2) 13. You invest $3,000 in an account. How long will it take for your account to grow to $20,000 if interest is compounded continuously at 3.3% per year? Give at least 3 decimal places in your answer and include units. (2) Math M119 Practice Test 1 page 5

6 14. The population of a small town was 350 in the year 2000 and grew to 670 in the year Write a formula for the population, P, as a function of t, where t is the number of years since 2000 if: a. the function is linear. P(t) = (2) b. the function is exponential. P(t) = (2) 15. Joe Slacker s grade is decreasing exponentially with a half life of 9 weeks. He starts the semester with 100%. How long will it take until his grade is down to 60%? Give at least 3 decimal places in your answer and include units. (3) 16. At 7 am, you drink a cup of coffee with 150 mg of caffeine. At 3 pm, 37 mg of caffeine remains in your system. Find the half life of caffeine. Give at least 3 decimal places in your answer and include units. (3) Math M119 Practice Test 1 page 6

CHAPTER 8. Consumer Mathematics and Financial Management Pearson Prentice Hall. All rights reserved.

CHAPTER 8. Consumer Mathematics and Financial Management Pearson Prentice Hall. All rights reserved. CHAPTER 8 Consumer Mathematics and Financial Management 2010 Pearson Prentice Hall. All rights reserved. 8.3 Compound Interest 2010 Pearson Prentice Hall. All rights reserved. 2 Objectives 1. Use the compound

More information

Investing Section 5.5

Investing Section 5.5 MATH 11009: Exponential Functions & Investing Section 5.5 Exponential Function: If b > 0, b 1, then the function f(x) = b x is an exponential function. The constant b is called the base of the function

More information

Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.

Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. MAC 1105 Final Review Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. 1) 8x 2-49x + 6 x - 6 A) 1, x 6 B) 8x - 1, x 6 x -

More information

Section 8.3 Notes- Compound Interest

Section 8.3 Notes- Compound Interest Section 8.3 Notes- Compound The Difference between Simple and Compound : Simple is paid on your investment or principal and NOT on any interest added Compound paid on BOTH on the principal and on all interest

More information

4.1 INTRODUCTION TO THE FAMILY OF EXPONENTIAL FUNCTIONS

4.1 INTRODUCTION TO THE FAMILY OF EXPONENTIAL FUNCTIONS Functions Modeling Change: A Preparation for Calculus, 4th Edition, 2011, Connally 4.1 INTRODUCTION TO THE FAMILY OF EXPONENTIAL FUNCTIONS Functions Modeling Change: A Preparation for Calculus, 4th Edition,

More information

Solving Compound Interest Problems

Solving Compound Interest Problems Solving Compound Interest Problems What is Compound Interest? If you walk into a bank and open up a savings account you will earn interest on the money you deposit in the bank. If the interest is calculated

More information

MATH 1108 MIDTERM EXAM MODEL SOLUTION

MATH 1108 MIDTERM EXAM MODEL SOLUTION MATH 1108 MIDTERM EXAM MODEL SOLUTION FALL 013 - MOON Name: FIDN#: Write your answer neatly and show steps. Except calculators, any electronic devices including a cell phone are not allowed. 1) Quick survey.

More information

Math 120 Final Exam Practice Problems, Form: A

Math 120 Final Exam Practice Problems, Form: A Math 120 Final Exam Practice Problems, Form: A Name: While every attempt was made to be complete in the types of problems given below, we make no guarantees about the completeness of the problems. Specifically,

More information

Round to Decimal Places

Round to Decimal Places Day 1 1 Round 5.0126 to 2 decimal 2 Round 10.3217 to 3 decimal 3 Round 0.1371 to 3 decimal 4 Round 23.4004 to 2 decimal 5 Round 8.1889 to 2 decimal 6 Round 9.4275 to 2 decimal 7 Round 22.8173 to 1 decimal

More information

MATH 34A REVIEW FOR MIDTERM 2, WINTER 2012. 1. Lines. (1) Find the equation of the line passing through (2,-1) and (-2,9). y = 5

MATH 34A REVIEW FOR MIDTERM 2, WINTER 2012. 1. Lines. (1) Find the equation of the line passing through (2,-1) and (-2,9). y = 5 MATH 34A REVIEW FOR MIDTERM 2, WINTER 2012 ANSWERS 1. Lines (1) Find the equation of the line passing through (2,-1) and (-2,9). y = 5 2 x + 4. (2) Find the equation of the line which meets the x-axis

More information

Percentages. It is quite straightforward to convert a percent into a fraction or decimal (and vice versa) using the following rules:

Percentages. It is quite straightforward to convert a percent into a fraction or decimal (and vice versa) using the following rules: What do percentages mean? Percentages Academic Skills Advice Percent (%) means per hundred. e.g. 22% means 22 per 00, and can also be written as a fraction ( 22 00 ) or a decimal (0.22) It is quite straightforward

More information

$496. 80. Example If you can earn 6% interest, what lump sum must be deposited now so that its value will be $3500 after 9 months?

$496. 80. Example If you can earn 6% interest, what lump sum must be deposited now so that its value will be $3500 after 9 months? Simple Interest, Compound Interest, and Effective Yield Simple Interest The formula that gives the amount of simple interest (also known as add-on interest) owed on a Principal P (also known as present

More information

Section Compound Interest. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section Compound Interest. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 11.3 Compound Interest INB Table of Contents Date Topic Page # June 16, 2014 Section 11.3 Examples 32 June 16, 2014 Section 11.3 Notes 33 2.3-2 What You Will Learn Compound Interest Present Value

More information

Lesson 6: Exponential Growth U.S. Population and World Population

Lesson 6: Exponential Growth U.S. Population and World Population : Exponential Growth U.S. Population and World Population Student Outcomes Students compare linear and exponential models of population growth. Classwork Example 1 (8 minutes) Give students time to review

More information

Week 2: Exponential Functions

Week 2: Exponential Functions Week 2: Exponential Functions Goals: Introduce exponential functions Study the compounded interest and introduce the number e Suggested Textbook Readings: Chapter 4: 4.1, and Chapter 5: 5.1. Practice Problems:

More information

MAT12X Intermediate Algebra

MAT12X Intermediate Algebra MAT12X Intermediate Algebra Workshop I - Exponential Functions LEARNING CENTER Overview Workshop I Exponential Functions of the form y = ab x Properties of the increasing and decreasing exponential functions

More information

ALGEBRA I (Common Core) Wednesday, June 17, :15 to 4:15 p.m., only

ALGEBRA I (Common Core) Wednesday, June 17, :15 to 4:15 p.m., only ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, June 17, 2015 1:15 to 4:15 p.m., only Student Name: School Name: The possession

More information

NAME: Date: Period: 2016 ALGEBRA 1 FALL SEMESTER EXAM REVIEW

NAME: Date: Period: 2016 ALGEBRA 1 FALL SEMESTER EXAM REVIEW NAME: Date: Period: 2016 ALGEBRA 1 FALL SEMESTER EXAM REVIEW Directions: Complete each multiple-choice question. Use your notebook, textbook and formula chart as reference material. 1. What is the range

More information

SEEM 2440A/B Engineering Economics First term, 2011 12. Midterm Examination

SEEM 2440A/B Engineering Economics First term, 2011 12. Midterm Examination SEEM 2440A/B Engineering Economics First term, 2011 12 Midterm Examination Instructions Exam Duration: 90 minutes Total Marks: 100 This examination paper comprises of THREE questions. Answer ALL questions.

More information

Key Economic Concepts: What is interest and how does it affect you?

Key Economic Concepts: What is interest and how does it affect you? Section 3 Financial Security Title of Lesson: Saving Accounts Prepared by: LaRee Misek Contact information: laree.misek@sendit.nodak.edu Time Allotment: 4 days Grade: Business Math Class Grades 10-11 Key

More information

January 22. Interest Rates

January 22. Interest Rates January 22 Interest Rates Compound Interest If you put $100 in a bank account at 5% interest per year, you will have $105 after one year. You earn $5 in interest. How much do you have after two years if

More information

Section 8.5 -Round answers to four decimal places.

Section 8.5 -Round answers to four decimal places. This last WIR is based on homework problems. Section 8.5 -Round answers to four decimal places. 1. a. Choose a sketch of the area under the standard normal curve corresponding to P(0.6 < Z < 1.8). a. b.

More information

Loans Practice. Math 107 Worksheet #23

Loans Practice. Math 107 Worksheet #23 Math 107 Worksheet #23 Loans Practice M P r ( 1 + r) n ( 1 + r) n =, M = the monthly payment; P = the original loan amount; r = the monthly interest rate; n = number of payments 1 For each of the following,

More information

8.3 Applications of Exponential Functions

8.3 Applications of Exponential Functions Section 83 Applications of Exponential Functions 789 83 Applications of Exponential Functions In the preceding section, we examined a population growth problem in which the population grew at a fixed percentage

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Math 1332 Exam Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the cardinal number for the set. 1) {10, 12, 14,..., 68} 1) Are the sets

More information

Final Exam Study Aid

Final Exam Study Aid Math 11 Final Exam Study Aid 1 of 39 Final Exam Study Aid Note: This study aid is intended to help you review for the final exam. It covers the primary concepts in the course. Although the final exam will

More information

MATHEMATICS MATH*1030 Final (Mock) Exam. Student #: Instructor: M. R. Garvie 24 Nov, 2015

MATHEMATICS MATH*1030 Final (Mock) Exam. Student #: Instructor: M. R. Garvie 24 Nov, 2015 FALL 2015 MATHEMATICS MATH*1030 Final (Mock) Exam Last name: (PRINT) First name: Student #: Instructor: M. R. Garvie 24 Nov, 2015 INSTRUCTIONS: 1. This is a closed book examination. Scientific and/or graphing

More information

Math of Finance Semester 1 Unit 2 Page 1 of 19

Math of Finance Semester 1 Unit 2 Page 1 of 19 Math of Finance Semester 1 Unit 2 Page 1 of 19 Name: Date: Unit 2.1 Checking Accounts Use your book or the internet to find the following definitions: Account balance: Deposit: Withdrawal: Direct deposit:

More information

CHAPTER FIVE. Solutions for Section 5.1. Skill Refresher. Exercises

CHAPTER FIVE. Solutions for Section 5.1. Skill Refresher. Exercises CHAPTER FIVE 5.1 SOLUTIONS 265 Solutions for Section 5.1 Skill Refresher S1. Since 1,000,000 = 10 6, we have x = 6. S2. Since 0.01 = 10 2, we have t = 2. S3. Since e 3 = ( e 3) 1/2 = e 3/2, we have z =

More information

Cost-Volume-Profit Analysis

Cost-Volume-Profit Analysis HOSP 2110 (Management Acct) Learning Centre Cost-Volume-Profit Analysis The basic principles of CVP analysis were covered in business math. CVP analysis can be done both graphically, through plotting the

More information

Main TVM functions of a BAII Plus Financial Calculator

Main TVM functions of a BAII Plus Financial Calculator Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there

More information

FINANCE m e p STRAND: FINANCE Unit 2 Simple and Compound Interest TEXT Section

FINANCE m e p STRAND: FINANCE Unit 2 Simple and Compound Interest TEXT Section CMM Subject Support Strand: FINANCE Unit 2 Simple and Compound Interest: Text m e p STRAND: FINANCE Unit 2 Simple and Compound Interest TEXT Contents Section 2.1 Simple Interest 2.2 Compound Interest 2.3

More information

MGF 1107 Spring 11 Ref: 606977 Review for Exam 2. Write as a percent. 1) 3.1 1) Write as a decimal. 4) 60% 4) 5) 0.085% 5)

MGF 1107 Spring 11 Ref: 606977 Review for Exam 2. Write as a percent. 1) 3.1 1) Write as a decimal. 4) 60% 4) 5) 0.085% 5) MGF 1107 Spring 11 Ref: 606977 Review for Exam 2 Mr. Guillen Exam 2 will be on 03/02/11 and covers the following sections: 8.1, 8.2, 8.3, 8.4, 8.5, 8.6. Write as a percent. 1) 3.1 1) 2) 1 8 2) 3) 7 4 3)

More information

What is the difference between simple and compound interest and does it really matter?

What is the difference between simple and compound interest and does it really matter? Module gtf1 Simple Versus Compound Interest What is the difference between simple and compound interest and does it really matter? There are various methods for computing interest. Do you know what the

More information

MATH 109 EXAM 2 REVIEW

MATH 109 EXAM 2 REVIEW MATH 109 EXAM REVIEW Remarks About the Exam: The exam will have some multiple choice questions ( 4-6 questions) AND some free response questions with multiple parts where you will have to show your work

More information

Algebra 2 Final Exam Review Ch 7-14

Algebra 2 Final Exam Review Ch 7-14 Algebra 2 Final Exam Review Ch 7-14 Short Answer 1. Simplify the radical expression. Use absolute value symbols if needed. 2. Simplify. Assume that all variables are positive. 3. Multiply and simplify.

More information

Percent, Sales Tax, & Discounts

Percent, Sales Tax, & Discounts Percent, Sales Tax, & Discounts Many applications involving percent are based on the following formula: Note that of implies multiplication. Suppose that the local sales tax rate is 7.5% and you purchase

More information

Finance 197. Simple One-time Interest

Finance 197. Simple One-time Interest Finance 197 Finance We have to work with money every day. While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for

More information

Section 5.2 The Natural Exponential Function

Section 5.2 The Natural Exponential Function Section 5.2 The Natural Exponential Function Objectives Identify the characteristics of the natural exponential function f(x) = e x, including the domain, range, intercept, asymptote, end behavior, and

More information

Pre-Session Review. Part 2: Mathematics of Finance

Pre-Session Review. Part 2: Mathematics of Finance Pre-Session Review Part 2: Mathematics of Finance For this section you will need a calculator with logarithmic and exponential function keys (such as log, ln, and x y ) D. Exponential and Logarithmic Functions

More information

ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only

ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The

More information

Also, compositions of an exponential function with another function are also referred to as exponential. An example would be f(x) = 4 + 100 3-2x.

Also, compositions of an exponential function with another function are also referred to as exponential. An example would be f(x) = 4 + 100 3-2x. Exponential Functions Exponential functions are perhaps the most important class of functions in mathematics. We use this type of function to calculate interest on investments, growth and decline rates

More information

Fractions, decimals and percentages

Fractions, decimals and percentages Fractions, decimals and percentages Some notes for the lesson. Extra practice questions available. A. Quick quiz on units Some of the exam questions will have units in them, and you may have to convert

More information

Math 21 Earning and Spending Money. Book 3: Interest. Teacher Version Assessments and Answers Included

Math 21 Earning and Spending Money. Book 3: Interest. Teacher Version Assessments and Answers Included Math 21 Earning and Spending Money Book 3: Interest Teacher Version Assessments and Answers Included Year Overview: Earning and Spending Money 1. Budget 2. Personal Banking 3. Interest 4. Consumer Credit

More information

Accounting & Finance Foundations Math Skills A Review. Place Value Percentages Calculating Interest Discounts Compounding

Accounting & Finance Foundations Math Skills A Review. Place Value Percentages Calculating Interest Discounts Compounding Accounting & Finance Foundations Math Skills A Review Place Value Percentages Calculating Interest Discounts Compounding Place Value Ten Thousands Thousands Hundredths Tenths Ones Tens Hundreds Thousands

More information

FINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA

FINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA FINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA 1.1 Solve linear equations and equations that lead to linear equations. a) Solve the equation: 1 (x + 5) 4 = 1 (2x 1) 2 3 b) Solve the equation: 3x

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Ch. 5 Mathematics of Finance 5.1 Compound Interest SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) What is the effective

More information

Math 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4)

Math 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4) Chapter 2: Functions and Linear Functions 1. Know the definition of a relation. Math 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4) 2. Know the definition of a function. 3. What

More information

n=number of interest periods per year (see the table below for more information) q=q(t)=q 0 e rt

n=number of interest periods per year (see the table below for more information) q=q(t)=q 0 e rt Compound interest formula P = the principal (the initial amount) A= r=annual interest rate (expressed as a decimal) n=number of interest periods per year (see the table below for more information) t=number

More information

6 Rational Inequalities, (In)equalities with Absolute value; Exponents and Logarithms

6 Rational Inequalities, (In)equalities with Absolute value; Exponents and Logarithms AAU - Business Mathematics I Lecture #6, March 16, 2009 6 Rational Inequalities, (In)equalities with Absolute value; Exponents and Logarithms 6.1 Rational Inequalities: x + 1 x 3 > 1, x + 1 x 2 3x + 5

More information

Grade 7 & 8 Math Circles. Finance

Grade 7 & 8 Math Circles. Finance Faculty of Mathematics Waterloo, Ontario N2L 3G1 Introduction Grade 7 & 8 Math Circles October 22/23, 2013 Finance A key point in finance is the time value of money, a concept which states that a dollar

More information

a b c d e You have two hours to do this exam. Please write your name on this page, and at the top of page three. GOOD LUCK! 3. a b c d e 12.

a b c d e You have two hours to do this exam. Please write your name on this page, and at the top of page three. GOOD LUCK! 3. a b c d e 12. MA123 Elem. Calculus Fall 2015 Exam 2 2015-10-22 Name: Sec.: Do not remove this answer page you will turn in the entire exam. No books or notes may be used. You may use an ACT-approved calculator during

More information

7-2 Solving Exponential Equations and Inequalities. Solve each equation y 3 = 4 y + 1 SOLUTION:

7-2 Solving Exponential Equations and Inequalities. Solve each equation y 3 = 4 y + 1 SOLUTION: Solve each equation. 2. 16 2y 3 = 4 y + 1 4. 49 x + 5 = 7 8x 6 6. A certificate of deposit (CD) pays 2.25% annual interest compounded biweekly. If you deposit $500 into this CD, what will the balance be

More information

ALGEBRA I (Common Core)

ALGEBRA I (Common Core) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, June 17, 2015 1:15 to 4:15 p.m. MODEL RESPONSE SET Table of Contents Question 25..................

More information

Week 1: Functions and Equations

Week 1: Functions and Equations Week 1: Functions and Equations Goals: Review functions Introduce modeling using linear and quadratic functions Solving equations and systems Suggested Textbook Readings: Chapter 2: 2.1-2.2, and Chapter

More information

7.1 Percent, Decimal and Fractions

7.1 Percent, Decimal and Fractions Chapter 7. Percent 7.1 Percent, Decimal and Fractions 7.2 Solving Percent Problems Using Percent Equations and Proportions 7.3 Application of Percent 7.4 Estimation with Percent 7.5 Interest 1 7.1 Percent,

More information

Prealgebra. Percent Change

Prealgebra. Percent Change Prealgebra 4 th Edition (Wyatt) Addendum to Chapter 5 Section 2 Percent formula: percent. (whole) = part Percent Change One of the most useful types of problems with percent deal with percent change. For

More information

Compounded Interest. Covers

Compounded Interest. Covers Compounded Interest Covers Section 3.3 Exponential Growth & Continuously Compounded Interest Section 4.3 Example: Continuously Compounded Interest (requires Integration) Section 3.3: Exponential Growth

More information

4 Percentages Chapter notes

4 Percentages Chapter notes 4 Percentages Chapter notes GCSE Specification concepts and skills Find a percentage of a quantity (N o): 4. Use percentages to solve problems (N m): 4., 4.2, 4., 4.4 Use percentages in real-life situations:

More information

Compound Interest. If you begin with P dollars (the principal), at the end of the first quarter you would have P dollars plus 2% of P dollars:

Compound Interest. If you begin with P dollars (the principal), at the end of the first quarter you would have P dollars plus 2% of P dollars: Compound Interest Compound Interest Money invested at compound interest grows exponentially. Banks always state annual interest rates, but the compounding may be done more frequently. For example, if a

More information

5.1 Simple and Compound Interest

5.1 Simple and Compound Interest 5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?

More information

Percent: Successive Changes (Compound Growth)

Percent: Successive Changes (Compound Growth) The Mathematics 11 Competency Test Percent: Successive Changes (Compound Growth) This short note is intended to emphasize that when the language of percent is used to describe a sequence of changes in

More information

16 21 Linear vs. Exponential.notebook May 14, 2014. LT 1c: I can compare linear vs. exponential change.

16 21 Linear vs. Exponential.notebook May 14, 2014. LT 1c: I can compare linear vs. exponential change. LT 1c: I can compare linear vs. exponential change. The Situation: You have $1,000 saved. Now, you need to figure out which bank you want to invest your money in. You can choose from the following two

More information

A percentage is a fraction with a denominator (bottom number) of % = 23

A percentage is a fraction with a denominator (bottom number) of % = 23 Chapter 5 Percentages We have all seen advertisements on television that use percentages. Shops selling items at a % discount or cereal boxes offering % more than usual for the same price. Percentages

More information

REVIEW SHEETS INTERMEDIATE ALGEBRA MATH 95

REVIEW SHEETS INTERMEDIATE ALGEBRA MATH 95 REVIEW SHEETS INTERMEDIATE ALGEBRA MATH 95 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts which are taught in the specified math course. The sheets

More information

Midterm Exam Study Guide

Midterm Exam Study Guide Class: Date: Midterm Exam Study Guide What is the product in simplest form? State any restrictions on the variable.. g 5 0h 2 h 5 0g 2 g h 00, g 0, h 0 g 7 00h, g 0, h 0 7 00 g h, g 0, h 0 d. 00 g 7 h

More information

Week 2 Quiz: Equations and Graphs, Functions, and Systems of Equations

Week 2 Quiz: Equations and Graphs, Functions, and Systems of Equations Week Quiz: Equations and Graphs, Functions, and Systems of Equations SGPE Summer School 014 June 4, 014 Lines: Slopes and Intercepts Question 1: Find the slope, y-intercept, and x-intercept of the following

More information

1. At what interest rate, compounded monthly, would you need to invest your money so that you have at least $5,000 accumulated in 4 years?

1. At what interest rate, compounded monthly, would you need to invest your money so that you have at least $5,000 accumulated in 4 years? Suppose your grandparents offer you $3,500 as a graduation gift. However, you will receive the gift only if you agree to invest the money for at least 4 years. At that time, you hope to purchase a new

More information

3.3 Applications of Linear Functions

3.3 Applications of Linear Functions 3.3 Applications of Linear Functions A function f is a linear function if The graph of a linear function is a line with slope m and y-intercept b. The rate of change of a linear function is the slope m.

More information

ALGEBRA I (Common Core) Monday, January 26, 2015 1:15 to 4:15 p.m., only

ALGEBRA I (Common Core) Monday, January 26, 2015 1:15 to 4:15 p.m., only ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Monday, January 26, 2015 1:15 to 4:15 p.m., only Student Name: School Name: The possession

More information

Chapter 12_Logarithms Word Problems

Chapter 12_Logarithms Word Problems The applications found here will mostly involve exponential equations. These equations will be solved using logarithms and their properties. Interest Problems Compound Interest If we start with a principal

More information

Math 201: Statistics November 30, 2006

Math 201: Statistics November 30, 2006 Math 201: Statistics November 30, 2006 Fall 2006 MidTerm #2 Closed book & notes; only an A4-size formula sheet and a calculator allowed; 90 mins. No questions accepted! Instructions: There are eleven pages

More information

Example 2: A company s car has an original value of $85, 000 and will be depreciated linearly over 6 years with scrap value of $10,000.

Example 2: A company s car has an original value of $85, 000 and will be depreciated linearly over 6 years with scrap value of $10,000. Section 1.5: Linear Models An asset is an item owned that has value. Linear Depreciation refers to the amount of decrease in the book value of an asset. The purchase price, also known as original cost,

More information

ALGEBRA I (Common Core) Wednesday, August 13, 2014 8:30 to 11:30 a.m., only

ALGEBRA I (Common Core) Wednesday, August 13, 2014 8:30 to 11:30 a.m., only ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, August 13, 2014 8:30 to 11:30 a.m., only Student Name: School Name: The

More information

a. all of the above b. none of the above c. B, C, D, and F d. C, D, F e. C only f. C and F

a. all of the above b. none of the above c. B, C, D, and F d. C, D, F e. C only f. C and F FINAL REVIEW WORKSHEET COLLEGE ALGEBRA Chapter 1. 1. Given the following equations, which are functions? (A) y 2 = 1 x 2 (B) y = 9 (C) y = x 3 5x (D) 5x + 2y = 10 (E) y = ± 1 2x (F) y = 3 x + 5 a. all

More information

Section 4.2 (Future Value of Annuities)

Section 4.2 (Future Value of Annuities) Math 34: Fall 2014 Section 4.2 (Future Value of Annuities) At the end of each year Bethany deposits $2, 000 into an investment account that earns 5% interest compounded annually. How much is in her account

More information

Financial Maths Investing Money

Financial Maths Investing Money Financial Maths Investing Money PD General Maths Name: C:\Documents and Settings\tracey_h-butters\Desktop\mathematics\year_levels\math_stage6\General\preliminary\notes\financial_maths\financia 1 CAPACITY

More information

Practice Problems to Prepare for Trades Math Assessment Test Form A (Answers are located at the end of this practice exam)

Practice Problems to Prepare for Trades Math Assessment Test Form A (Answers are located at the end of this practice exam) Practice Problems to Prepare for Trades Math Assessment Test Form A (Answers are located at the end of this practice exam) The actual Trades Math Assessment Test will have 0 questions few multiple choice

More information

Exponential Functions and Their Graphs

Exponential Functions and Their Graphs Exponential Functions and Their Graphs Definition of Exponential Function f ( x) a x where a > 0, a 1, and x is any real number Parent function for transformations: f(x) = b a x h + k The graph of f moves

More information

MATH 111: EXAM 02 SOLUTIONS

MATH 111: EXAM 02 SOLUTIONS MATH 111: EXAM 02 SOLUTIONS BLAKE FARMAN UNIVERSITY OF SOUTH CAROLINA Answer the questions in the spaces provided on the question sheets and turn them in at the end of the class period Unless otherwise

More information

Math Review Sheets Math 20 Basic Mathematics (Arithmetic)

Math Review Sheets Math 20 Basic Mathematics (Arithmetic) Math Review Sheets Math 0 Basic Mathematics (Arithmetic) The purpose of this Review Sheet is to provide students a comprehensive review of items that are taught in Math 0 classes. It is the KCC Math Department

More information

ALGEBRA I (Common Core) Thursday, June 16, 2016 9:15 a.m. to 12:15 p.m., only

ALGEBRA I (Common Core) Thursday, June 16, 2016 9:15 a.m. to 12:15 p.m., only ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, June 16, 2016 9:15 a.m. to 12:15 p.m., only Student Name: School Name:

More information

20(-1) - (-4) (-5) 10)

20(-1) - (-4) (-5) 10) Pre-Algebra Final Exam Review Name Write the whole number in words. 1) 9,300,695 1) Add. 2) 58,142 30,645 + 5,300,621 2) Round the whole number to the given place. 3) 49,815,425 to the nearest million

More information

originally cost, r is the interest rate as a decimal, and t is the time in years. [A] $26.34 [B] $4.71 [C] $3.67 [D] $5.59

originally cost, r is the interest rate as a decimal, and t is the time in years. [A] $26.34 [B] $4.71 [C] $3.67 [D] $5.59 1. The inflation rate of the U.S. dollar is 3 percent. This means that every year prices increase by 3 percent. If a sandwich cost $4.45 five years ago, what does it cost now? Use the the amount an item

More information

Oil prices rise by 4% The numerator is 45 and the denominator is 100

Oil prices rise by 4% The numerator is 45 and the denominator is 100 2 CHAPTER 3. 3 A head Scatter graphs CHAPTER 3 Percentages CHAPTER 2. Percentages ALL PRICES REDUCED BY % DAILY BLAH Oil prices rise by 4% thank you for your contribution this year. Your salary will increase

More information

The Mathematics 11 Competency Test Percent Increase or Decrease

The Mathematics 11 Competency Test Percent Increase or Decrease The Mathematics 11 Competency Test Percent Increase or Decrease The language of percent is frequently used to indicate the relative degree to which some quantity changes. So, we often speak of percent

More information

2. In solving percent problems with a proportion, use the following pattern:

2. In solving percent problems with a proportion, use the following pattern: HFCC Learning Lab PERCENT WORD PROBLEMS Arithmetic - 11 Many percent problems can be solved using a proportion. In order to use this method, you should be familiar with the following ideas about percent:

More information

Math. Rounding to Tens & Hundreds. Answers. 1) Round to the nearest Hundred ) Round to the nearest Hundred. 829

Math. Rounding to Tens & Hundreds. Answers. 1) Round to the nearest Hundred ) Round to the nearest Hundred. 829 1) Round to the nearest Hundred. 455 2) Round to the nearest Hundred. 829 3) Round to the nearest Hundred. 7,444 4) Round to the nearest Ten. 23,349 5) Round to the nearest Hundred. 759 6) Round to the

More information

FINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

FINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. FINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether or not the relationship shown in the table is a function. 1) -

More information

CHAPTER 3. Exponential and Logarithmic Functions

CHAPTER 3. Exponential and Logarithmic Functions CHAPTER 3 Exponential and Logarithmic Functions Section 3.1 (e-book 5.1-part 1) Exponential Functions and Their Graphs Definition 1: Let. An exponential function with base a is a function defined as Example

More information

Exponential growth and decay

Exponential growth and decay A Exponential growth and decay On the same day two friends both buy a foal. Both foals have a weight of 50 kilogram. After one month they compare the weights. Fred says, "My foal grew 10 kg." Andy answers,

More information

Percentages. Examination Question: A car was bought for It depreciated in value by 25% each year. What was the value of the car after 3 years?

Percentages. Examination Question: A car was bought for It depreciated in value by 25% each year. What was the value of the car after 3 years? Percentages Percentages Multipliers The multiplier for an increase of 6% is 1.06 (100% + 6% = 106% or 1.06). To increase an amount by 6%, multiply it by 10.06. The multiplier for a decrease of 12% is 0.88

More information

Name: Exam III. April 16, 2015

Name: Exam III. April 16, 2015 Department of Mathematics University of Notre Dame Math 10120 Finite Math Spring 2015 Name: Instructors: Garbett & Migliore Exam III April 16, 2015 This exam is in two parts on 10 pages and contains 15

More information

Section 1.5 Linear Models

Section 1.5 Linear Models Section 1.5 Linear Models Some real-life problems can be modeled using linear equations. Now that we know how to find the slope of a line, the equation of a line, and the point of intersection of two lines,

More information

7.2 Compound Interest

7.2 Compound Interest 7.2 Compound Interest For compound interest, the interest is reinvested at regular intervals. The interest is added to the principal to earn interest for the next interval of time, or compounding period.

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) - 19

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) - 19 Math 100 Review for the Final Examination MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) -1[7x + 6-7(x + 1)] = -4x - 6 1)

More information

Sample problems from Chapter 10.1

Sample problems from Chapter 10.1 Sample problems from Chapter 10.1 This is the annuities sinking funds formula. This formula is used in most cases for annuities. The payments for this formula are made at the end of a period. Your book

More information

1. Annuity a sequence of payments, each made at equally spaced time intervals.

1. Annuity a sequence of payments, each made at equally spaced time intervals. Ordinary Annuities (Young: 6.2) In this Lecture: 1. More Terminology 2. Future Value of an Ordinary Annuity 3. The Ordinary Annuity Formula (Optional) 4. Present Value of an Ordinary Annuity More Terminology

More information

Math 1303: Practice Exam 3

Math 1303: Practice Exam 3 . What is the meaning of the following symbols: a) f() d indefinite integral or antiderivative Math 303: Practice Eam 3 b b) f() d a Definite integral or area under a curve (if f() >= 0). Find the following

More information

MM 6-1 MM What is the largest number you can make using 8, 4, 6 and 2? (8,642) 1. Divide 810 by 9. (90) 2. What is ?

MM 6-1 MM What is the largest number you can make using 8, 4, 6 and 2? (8,642) 1. Divide 810 by 9. (90) 2. What is ? MM 6-1 1. What is the largest number you can make using 8, 4, 6 and 2? (8,642) 2. What is 500 20? (480) 3. 6,000 2,000 400 = (3,600). 4. Start with 6 and follow me; add 7, add 2, add 4, add 3. (22) 5.

More information