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