Mathematics Algebra II Unit 13: Exploring a Business Venture

Transcription

1 Mathematics Algebra II Unit 13: Exploring a Business Venture

2 1 Janice proposed a business plan, for an advertising company, to a bank that provides qualified applicants with small business loans. The graph below illustrates projected sales for the first year. What is the range of monthly sales of the online companies, n, compared to the range of the offline companies, f? A $6000 n $22,000 $6000 f $32,000 B $6000 f $22,000 $6000 n $32,000 C $6000 f $22,000 $6000 n $32,000 D $6000 n $22,000 $6000 f $32,000 Page 2

3 2 The function f(x) = 502(1.175) x models the projected first year revenue from an officeassistance service, where f(x) represents the total revenue, and x is the number of months. If this pattern continues, what is the projected revenue to the nearest dollar for the 2 months past year one? Page 3

4 3 Beth proposed a business plan, for an advertising company, to a bank that provides qualified applicants with small business loans. Included in her plan is the sale of marketing mouse pads. The following graph illustrates the break even analysis projected for the monthly sales of the mouse pads after fixed and total costs. Given the system of equations for total costs and sales, how much money in sales must Beth earn to break even? A $5,000 B $19,500 C $20,000 D $25,000 Page 4

5 4 The table below illustrates highlights of her business plan, including projected sales, s, and net profit, p. Year (n) Sales (s) Net Profit (p) 1 $200,000 $25,000 2 $350,000 $75,000 3 $500,000 $125,000 Write a system of linear equations in function notation that can be used to model projected sales, s, and net profit, p. 5 Mandy bought a desktop computer system, to start her business from home, for $4,995. It is expected to depreciate at a rate of 11.5% per year. What will be the value of the computer system in 3 years? Round your answer to the nearest dollar. A $4,421 B $3,802 C $3,462 D $2,812 Page 5

6 6 John recorded the following cash flow per month of the first year of business at his new advertising company. He uses the function f(x) = 0.025x x x to model the cash balance data and makes predictions beyond year 1. Given this information, what can John project as the amount of cash flow in the 18 th month of operation? F $162,000 G $126,000 H $111,000 J $89,000 Page 6

7 7 Melissa expands her initial marketing plan to include an office assistance service to companies. The table below presents the monthly charge for this service, presenting data that yields an exponential function. Monthly Revenue Month Charge Month 1 $400 Month 2 $700 Month 3 $900 Month 4 $1,100 Month 5 $1,300 Month 6 $1,600 Month 7 $1,700 Month 8 $1,900 Month 9 $2,000 Month 10 $2,400 Month 11 $2,800 Month 12 $3,200 Describe the limitation on the domain of the data. 8 The function P = 20s 2 + 1,400s 12,000 models the profit, P, from selling merchandise at s price. What is the selling price that generates the maximum profit? F $12,500 G $1,200 H $35 J $10 Page 7

8 Use the information and the graph below to answer the following two questions. The following graph illustrates the break even analysis projected for monthly sales of a new company. 9 Which is the best equation that can be used to represent the given data if the domain, s, represents sales, and the range, f(s), represents profits? A f(s) = s 19,474 B f(s) = 5s 2 2s + 21,571 C f(s) = 1s + 19,474 D f(s) = 5s 2 + 2s 21, How does the Break Even Analysis graph compare to the graph of its parent function? F The Break Even Analysis graph is translated below the graph of the parent function. G The Break Even Analysis graph is translated above the graph of the parent function. H The Break Even Analysis graph is steeper than the graph of the parent function. J The Break Even Analysis graph is less steep than the graph of its parent function. Page 8 STOP

9 Test Key Mathematics Algebra II Unit 13: Exploring a Business Venture ## Item # Correct Answer Primary SE Secondary SE Obj/Cat 1 ALG224993CS B A2.1(A) [R] None 1 2 ALG225001CS 4800 A2.11(C) [S] None 7 3 ALG224999CS D A2.3(B) [R] None 4 ALG224998CS 0 to 2 A2.3(A) [R] None ALG225002CS C A2.11(F) [R] None 7 6 ALG224997CS F A2.2(A) [S] None 2 7 ALG225000CS Clients may purchase this office-assistance service for a full month at a time, from one month, up to a full year. A2.11(B) [S] None 7 8 ALG225003CS H A2.8(D) [R] None 9 ALG224994CS A A2.1(B) [R] None 10 ALG224996CS F A2.4(B) [R] None 3 1 1

10 Scoring Rubrics 4 s = $50,000 + $150,000n p = 25, ,000n