MATH 2070 Test 1 (Sections )

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1 Multiple Choice: Use a # pencil and completely fill in each bubble on your scantron to indicate the answer to each question. Each question has one correct answer. If you indicate more than one answer, or leave a blank, the question will be marked as incorrect. In this section there are 13 multiple choice questions. Each question is worth 3 points for a total of 39 points. For future reference, circle your answers on this test paper as you will not receive your Scantron back with your test. 1. The rate of change of the per capita consumption of Greek yogurt, in ounces per year, in the U.S. between and 15 is shown in the figure below. Find the total change in the per capita consumption of Greek yogurt in the U.S. between and 15. a. 4 ounces b. 48 ounces c. 168 ounces d. 19 ounces The rate of change of the temperature of a bottle of white wine that has been placed in a.6h refrigerator is given by w( h) 18e per hour, h hours after the bottle is placed in the refrigerator. Check: w() By how many degrees will the temperature of the wine have dropped after 3 hours in the refrigerator? a b c d d 3. Given F is an antiderivative of f, f ( t) dt =. 3 a. F (5) F (3) b. c. f (5) d. f (5) C 3

2 The rate of change of the amount of Medicare funds spent on hospice care between 1989 and 1997 can be modeled by m( t).67t.e.67t 13 e billion dollars per year, where t is the number of years after 1989, t 8. Check: m(5) Use this information to answer the net five questions. 4. If the area between m( t ) and the t ais from t to t 8 were to be estimated using four right rectangles of equal width, what is the height of the tallest rectangle? a b..73 c d Estimate the area between m( t ) and the t ais from t to t 8 using two midpoint rectangles. a..83 b c d Which of the following is a TRUE statement about the accumulation function a. M ( ) is always concave down on the interval from t to t 8. b. M ( ) has a relative maimum at t 4. M ( ) m( t) dt? c. M ( ) has an inflection point at t 4. d. M ( ) is always concave up on the interval from t to t 8. 4

3 7. Interpret m(5) a. By 1994, the amount of Medicare funds spent on hospice care had increased by billion dollars. b. In 1994, the amount of Medicare funds spent on hospice care was increasing by billion dollars per year. c. In 1994, the rate of change in the amount of Medicare funds spent on hospice care was increasing by billion dollars per year. d. By 1994, the change in the amount of Medicare funds spent on hospice care had increased by billion dollars. 8. If the value of 8 m( t) dt was known, what other information is needed to determine the amount of Medicare funds spent on hospice care in 1997? a. the amount of Medicare funds spent on hospice care in b. the rate of change of the amount of Medicare funds spent on hospice care in c. the rate of change of the amount of Medicare funds spent on hospice care in d. the rate of change of the amount of Medicare funds spent on hospice care for the years 1989 through Given that F is an antiderivative of f, and F ( b) 45, F ( a) 1, f ( b) 14 and f ( a) 5. b Determine the value of f ( ). a. 9 b. 19 c. 35 d. 55 a 5

4 1. Which of the following epressions represents the total area of the region between the graph of f ( ) 7 1 and the -ais from a = to b = 3. Check: f (4) a. b. c. 3 f ( ) f ( ) 3 f ( ) 1 3 f ( ) f ( ) f ( ) 1 d. 3 f ( ) f ( ) 11. a C b. ln 5 c. d. 1 ln 5 C C C 1. d t e ln( t) dt a. e ln( ) b. e ln( ) C c. e ln( ) e ln() d. e 1 C 6

5 13. The rate of change of the total number of acres of genetically modified crops grown worldwide from 1997 to 3 is given by r( t).43t 15.38t million acres/year, t years since Check: r() 8.65 The total number of acres of such crops grown in 1997 (t = ) was 35.5 million acres. How many acres of genetically modified crops were grown worldwide in 3 ( t 6 )? a. 3.7 million acres b million acres c million acres d million acres Check your Scantron now to make sure it will successfully run. Refer to the last page of the test for specifics. If it does, you will earn one point. (1 pt) When you are not working on the multiple choice portion of the test, turn your Scantron over so that it cannot be read by others in the room. 7

6 RE-READ the directions on the second page of the test regarding rounding, units, etc. Then read each question carefully. Provide only one clearly indicated answer to each question. If your answer is illegible, it will be graded as incorrect. Show all work. This portion is 6%. 1. The number of cats living on a large college campus was changing at a rate of r( t ) cats per year, t years after 1, t 5. t 1.4(1.77 ) a. The general antiderivative of r( t ) is R( t) r( t) dt C. Use the fact that ln(1.77) there were 85 cats on campus in 1 to find the specific antiderivative model. Show your work in the space provided and then complete the model below. Round any computed values to three decimal places. (6 pts) R( t) gives the function output description units t years after 1, t 5. b. Determine the change in the on-campus cat population between 1 and 13. Show the mathematical notation and your answer rounded in contet with units. (3 pts) 8

7 . The rate of change in the weight of a person is given by w( ).4.56 pounds per week where is the number of weeks since the person began dieting,. Check: w().96 a. Find the total area trapped between the graph of w( ) and the -ais on the interval from = to =. Show the mathematical notation used to find your answer. Round your answer to three decimal places. (5 pts) b. Consider the contet of the problem. If this person weighed 18 pounds at the start of the diet, how much did the person weigh at the end of the -week period? Show enough work/ mathematical notation to justify your answer. Round your answer to three decimal places. Answer: pounds (5 pts) Work/Notation: c. Complete the following statements with the correct number. (7 pts) i. The person s weight was at a relative minimum weeks after the diet began. ii. The person s weight was decreasing most rapidly weeks after the diet began. iii. Was the person s weight higher at = 7 weeks or = 14 weeks? d. On what interval would the accumulation function t A( t) w( ) be increasing at a faster rate? Answer: < t < ( pts) (give the largest interval possible) e. On what interval would the accumulation function Answer: < t < (give the largest interval possible) t A( t) w( ) be concave up? ( pts) 9

8 3. Find each of the following. Use proper notation throughout your work. You do not need to simplify your coefficients. (4 pts each = 1 pts). a. 5 b. 4 3 e e e c Algebraically evaluate the following integral to obtain the eact answer. (7 pts) Show each step necessary to obtain the answer algebraically using proper notation throughout your work. Simplify fractions. i.e. 17 should be simplified to 15 which should be simplified to Do not approimate values such as 1 3. Keep all values eact. Combine like terms and simplify when possible

9 5. The rate of change of the population of a city between 195 and 1995 is shown in the graph. a. Fill out the table below. (5 pts) A( ) f ( t) dt b. Use the aes and the values in the table to graph the accumulation function A( ) f ( t) dt on the interval 9. (6 pts) Label any relative maimum, RMa and any relative minimum, RMin. Label any inflection point, IP. Correctly represent the concavity. 11

MATH 2070 Test 1 (Sections )

MATH 2070 Test 1 (Sections ) MATH 070 Test 1 (Sections 5.1 5.6) Spring 018 Multiple Choice: Use a # pencil and completely fill in each bubble on your scantron to indicate the answer to each question. Each question has one correct