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Exam #1A Name Math M119 (Spring, 2013) Score /60 = % 1. Use the function graphed below to answer the questions… Note: Each question only has one correct answer a. Name an interval that is both increasing and concave down. , , , b. Name an interval that is both decreasing and concave up. , , , c. The interval is CONCAVE UP, CONCAVE DOWN, INCREASING, DECREASING d. The interval is CONCAVE UP, CONCAVE DOWN, INCREASING, DECREASING (1) (1) (1) (1) 2 Using the data in the table below, write t as a linear function of r r ‐4 1 3 8 t 9.5 0.75 ‐2.75 ‐11.5 Write your answer in slope-intercept form (3) D B C E A3. Find the average rate of change of x31 between x = -2 and x = 1 You may either leave your answer in exact form or round to 3 decimal places. (3) 4. Find the relative rate of change of lnx between x = 3 and x = 4 You may either leave your answer in exact form or round to 3 decimal places. (3) 5. The table below gives sales of a local microbrewery (in millions of dollars). Year 2002 2003 2004 2005 2006 Sales 2.40 2.85 3.23 3.63 3.76 a. Find the net change in sales between 2002 and 2005. b. Find the average rate of change in sales between 2003 and 2006. c. Find the relative rate of change of sales between 2003 and 2004. a. (2) b. (2) c. (2)6. A company has cost and revenue functions shown below 9 600 and 15 a. Find the total revenue when q = 85 units b. Find the marginal cost of production? c. Find the total profit function, P(q). Simplify as much as possible. d. For what quantity produced will the company break-even? a. (1) b. (1) c. (2) d. (2) 7. Using the graphs of the supply and demand function shown below… Hint: Tick marks on the horizontal axis are spaced 125 units apart. Tick marks on the vertical axis are spaced $50 apart. a. How many units will consumer purchase when the price is $500? b. At what price will manufacturers produce a quantity of 625 units? c. Give the coordinates of the equilibrium point. a. (1) b. (1) c. (2)8. The price of a share of LinEx stock is currently $150. Write a formula for the price, P, as a function of time t if… a. The price of the stock increases $12 per year. b. Using your answer from part a, estimate the price of a share of stock in 4 years c. The price of the stock increases annually at a rate of 8% per year . d. Using your answer from part c, estimate the price of a share of stock in 6 years a. (2) b. (1) c. (2) d. (1) 9. The table below represents an exponential function of the form ∙… t ‐1 0 1 2 P 52.17 60 69 79.35 a. Find the percent rate of growth/decay. Include the appropriate sign (+ or -) b. Write the an exponential function in the form ∙ a. (2) b. (1)10. Find the function, in the form taPP0 , that best describes the graph below. When finding the value a, round to the nearest 0.01 (i.e. the 2nd decimal place) (3) 11. Solve for t: Give exact answers only 35 (3) 12. Convert the function teP20.08to the form taPP (Round the value a to three decimal places) (2) 13. What continuous decay rate, expressed as a decimal, is equivalent to an annual decay rate of 25%? Round the percentage to one decimal place. (2) 14. Suppose $5000 is invested in a saving account that pays interest at a rate of 4.5% per year. If the interest is compounded annually, find the amount in the account after 10 years. (Round to the nearest cent – i.e. two decimal places) (3) t P 27 (3, 8)15. The value of a retirement annuity doubles every 9.25 years. Assuming it grows exponentially at a continuous rate, find the growth rate. (Round to 3 decimal places) (3) 16. You need $10,000 in your account 3 years from now and the interest rate is 8% per year, compounded annually. How much should you deposit now to reach your goal in 3 years? (Round to the nearest cent – i.e. two decimal places) (3) 17. A substance decays continuously at a rate of 12 percent hour. How many hours will it take for the substance to be reduced to half its initial size? (Round to 1 decimal place) (3) 18. The population of a city is increasing exponentially at a continuous rate of 2.6% per year. In 2010, the city’s population was 100 thousand people. In how many years will the population reach 120 thousand people? (Round to 1 decimal place)

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