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IUPUI MATH 119 - Exam1_Review

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Exam #1 In-Class Review M119 1. For the functionxxxf 32)( between 2x and1x. 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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