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Exam #1 In-Class Review M119 1. For the functionxxxf 32)( between 2x and1x. a. Find the average rate of change. b. Find the relative rate of change. 2. Use the values in the following table to express q as a linear function of p. p 3 7 11 15 q 18 13 8 3 3. The following table gives values of a function ).(tfw Is the function… t 5 10 15 20 w 2 10 16 18 a. increasing or decreasing? b. concave up or concave down? 4. Find the relative change of the population of a town if it decreases from 1425 to 1360. Write your answer as a percent with at least 2 decimal places.5. A company that makes backpacks has fixed costs of $1600 and variable costs of $23 per backpack. The company sells the backpacks for $45 each. a. Write the (total) cost function C(q) = b. Write the (total) revenue function R(q) = c. Find and simplify the profit function P(q) = d. Find the marginal profit (per backpack) $ e. How many backpacks would need to be sold to break even? 6. Solve for x. Give at least 3 decimal places in your answers. a. 57 x b. xe49 7. A product costs $480 today. Write an expression for the cost in t days if the price is reduced by: a. $4 a day b. 4% a day 8. Determine if the function is linear, exponential or neither. Find a formula for the function. x 4 5 6 7 f(x) 20 14 8 29. A city’s population is 28,000 and growing at 2.5% per year. Estimate the population 12 years from now if the 2.5% is: a. an annual rate b. a continuous annual rate 10. What continuous percent growth rate is equivalent to an annual percent growth rate of 13%? Give at least 3 decimal places in your answer. 11. If you deposit $900 into an account earning interest at a rate of 1.5% per year, write an expression for the amount in the account t years from now if the interest is compounded annually and find the balance in 20 years. 12. If $600 is deposited into an account paying interest at a rate of 5% per year, compounded continuously, how long does it take for the balance in the account to reach $2100? Give at least 3 decimal places in your answer. 13. You want to accumulate $30,000 in 15 years. How much should you invest now if you expect the investment to grow at a rate of 4% per year, compounded annually? Give your answer to the nearest cent.14. You invest $7000 in an account which pays interest compounded continuously. If you want the account to be worth $15,000 in 11 years, what continuous annual interest rate do you need? 15. How long will it take for your money to double if it is invested at 3.75% compounded annually? Include units in your answer. 16. We have 40 grams of a substance that has a half-life of 15 years. Find the decay rate and determine the amount of the substance that remains in 10 years 17. You take 200 mg of a medication at 8 am. If the medication decays at a rate of 20% per hour, at approximately what time will only 100 mg

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