MATH 2070 Test 1 (Sections 5.1 – 5.7) Fall 2015 Version A KEY Multiple Choice: Use a #2 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 15 multiple choice questions. Each question is worth 3 points for a total of 45 points. For future reference, circle your answers on this test paper as you will not receive your Scantron back with your test. ______________________________________________________________________________ ( )p t gives the rate of change of profit for Lollipop Kids hair salon in thousand dollars per year, where t is the number of years after 2000. The graph of ( )p t is shown below. Use the graph of ( )p t to answer the next three questions. 1. In what year was the profit at a relative minimum? a. 2000 b. 2006 c. 2009 d. 2008 2. At what t-value was the profit decreasing most rapidly? a. 7.75t  b. 4.5t  c. 6t  d. 9t  3. Which of the following describes the shape of the graph of the accumulation function 0( ) ( )xA x p t dt between x = 4 and x = 6? a. decreasing and concave up b. increasing and concave down c. increasing and concave up d. decreasing and concave down ______________________________________________________________________________ t years after 2000 p(t) thousand dollars per year Rate of Change of ProfitMATH 2070 Test 1 (Sections 5.1 – 5.7) Fall 2015 Version A KEY ______________________________________________________________________________ The number of people watching TV on mobile phones from 2007 to 2011 grew at a rate of 5.4145( )1 0.91n tt million people per year, t years since 2007. Check: (2) 3.224n Use this information to answer the next four questions. 4. Which of the following is the correct interpretation of (2) 3.224n? “In 2009, the number of people watching TV on mobile phones ____________________.” a. …was decreasing by 3.224 million people per year. b. …was increasing by 3.224 million people per year. c. …increased by 3.224 million people. d. …was 3.224 million people. 5. Which of the following is the correct interpretation of 40( ) 13.733n t dt ? “From 2007 to 2011, ________________________________________________________.” a. the rate of change in the number of people watching TV on mobile phones was increasing by 13.733 million people per year. b. the number of people watching TV on mobile phones was increasing by 13.733 million people per year. c. the rate of change in the number of people watching TV on mobile phones increased by 13.733 million people. d. the number of people watching TV on mobile phones increased by 13.733 million people. 6. If the area trapped between ( )n t and the t-axis from 0t to 4t were to be estimated using four right rectangles of equal width, what would the height of the tallest rectangle be? a. 5.415 b. 3.918 c. 3.932 d. 5.327 7. Estimate the area trapped between ( )n t and the t-axis from 0t to 4t using two midpoint rectangles of equal width. a. 11.476 b. 17.278 c. 6.721 d. 13.443 ______________________________________________________________________________MATH 2070 Test 1 (Sections 5.1 – 5.7) Fall 2015 Version A KEY ______________________________________________________________________________ 8. Find the specific antiderivative ( )F x, given 2( ) 3 4 1f x x x   and (1) 9F. a. 3 2( ) 2 7F x x x x    b. 3 2( ) 2 9F x x x   c. 3 2( ) 2 9F x x x x    d. 3 2( ) 2 6F x x x   ______________________________________________________________________________ Entomologists studied the female and male populations of ladybugs in a botanical garden over an 8-month period. They found that the female population was changing at a rate of 2( ) .8 8 25f x x x   thousand ladybugs per month and the male population was changing at a rate of 2( ) .6 3.6 7.4m x x x    thousand ladybugs per month, where x is the number of months since they first began observing the population. The graph of their findings is shown below. Check: (3) 8.2 (3) 12.8f and m  Use this information to answer the next three questions. 9. Which of the following calculates the total combined area of the regions marked A and B? a.    2 6.2860 2( ) ( ) ( ) ( )f x m x dx m x f x dx    b.  6.2860( ) ( )f x m x dx c.    2 6.2860 2( ) ( ) ( ) ( )f x m x dx m x f x dx    d.  6.2860( ) ( )f x m x dxMATH 2070 Test 1 (Sections 5.1 – 5.7) Fall 2015 Version A KEY Context continued from previous page. The graph is repeated for your convenience. 10. Find the area of the shaded region of the graph marked A. a. 20.4 b. 56.533 c. 36.133 d. 15.733 11. Which of the following is the correct interpretation of area A found in the previous question? a. During the first two months the increase in the female population was A thousand lady bugs greater than the increase in the male population. b. During the first two months the increase in the male population was A thousand ladybugs more than the increase in the female population. c. After two months, the female population was A thousand ladybugs greater than the male population. d. After two months, the male population was A thousand ladybugs greater than the female population. ______________________________________________________________________________ 12. The rate of change in the net earnings of Gap, Inc., from 1990 through 2001 is shown in the figure. Determine by how much Gap, Inc. earnings changed between 1990 and 2001. a. – 420.88 million dollars b. – 433.69 million dollars c. – 488.675 million dollars d. – 475.038 million dollars