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48. Our ruby-throated hummingbird has entered another patch of flowers, and the energy she is getting as a function of time in the patch is plotted below. 2,000 1,600 1,200 800 400 10 20 30 40 50 60 a. Find the average energy intake rate. b. Estimate at what time the instantaneous energy intake rate equals the average intake rate.

48. Our ruby-throated hummingbird has entered another patch of flowers, and the energy she is getting as a function of time in the patch is plotted below. 2,000 1,600 1,200 800 400 10 20 30 40 50 60 a. Find the average energy intake rate. b. Estimate at what time the instantaneous energy intake rate equals the average intake rate.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 48

45. To study the response of nerve fibers to a stimulus, a biologist models the sensitivity, S, of a particular group of fibers by the function a. Estimate N'(t) for 0 < t < 17. b. Graph N'(t) and briefly interpret this graph. for 0 <t < 3 9 for t > 3 t 48. Our ruby-throated hummingbird has entered another patch of flowers, and the energy she is getting as a function of time in the patch is plotted f(t) = below. where t is the number of days since the excitation began. a. Over what time period is sensitivity increasing? When is it decreasing? y 2,000 b. Graph S'(t). 1,600 46. During the time period 1905–1940, hunters virtually wiped out all large predators on the Kaibab Plateau near the Grand Canyon in northern Arizona. The data for the deer population, P, over this period of 1,200 800 400 time are as follows: Year Deer population Year Deer population 10 20 30 40 50 60 1905 4,000 9,000 25,000 65,000 100,000 60,000 40,000 1927 37,000 1910 1928 35,000 a. Find the average energy intake rate. 1915 30,000 25,000 1929 1920 1930 b. Estimate at what time the instantaneous energy 1924 1931 intake rate equals the average intake rate. 20,000 18,000 1925 1935 49. Two radar patrol cars are located at fixed positions 6 miles apart on a long, straight road where the speed limit is 65 miles per hour. A sports car passes the first patrol car traveling at 60 miles per hour; then 5 minutes later, it passes the second patrol car going 65 miles per hour. Analyze this situation to show that at some time between the two clockings, the sports car exceeded the speed limit. Hint: Use the MVT. 1926 1939 10,000 Source: www.biologycorner.com/worksheets/kaibab.html a. Estimate P'(t) for 1905 <t< 1939. b. Graph and interpret P'(t). 47. In 1913, Carlson studied a growing culture of yeast (see Problem 45 in Problem Set 2.4 and Section 6.1). The table of population densities N(t) at one-hour intervals is shown here: 50. Suppose two race cars begin at the same time and finish at the same time. Analyze this situation to show that at some point in the race they had the same speed. Time Population Time Population Time Population 9.6 6. 174.6 12 594.8 1 18.3 7 257.3 13 629.4 20.0 250 7 14 640 8
Transcribed Image Text:45. To study the response of nerve fibers to a stimulus, a biologist models the sensitivity, S, of a particular group of fibers by the function a. Estimate N'(t) for 0 < t < 17. b. Graph N'(t) and briefly interpret this graph. for 0 <t < 3 9 for t > 3 t 48. Our ruby-throated hummingbird has entered another patch of flowers, and the energy she is getting as a function of time in the patch is plotted f(t) = below. where t is the number of days since the excitation began. a. Over what time period is sensitivity increasing? When is it decreasing? y 2,000 b. Graph S'(t). 1,600 46. During the time period 1905–1940, hunters virtually wiped out all large predators on the Kaibab Plateau near the Grand Canyon in northern Arizona. The data for the deer population, P, over this period of 1,200 800 400 time are as follows: Year Deer population Year Deer population 10 20 30 40 50 60 1905 4,000 9,000 25,000 65,000 100,000 60,000 40,000 1927 37,000 1910 1928 35,000 a. Find the average energy intake rate. 1915 30,000 25,000 1929 1920 1930 b. Estimate at what time the instantaneous energy 1924 1931 intake rate equals the average intake rate. 20,000 18,000 1925 1935 49. Two radar patrol cars are located at fixed positions 6 miles apart on a long, straight road where the speed limit is 65 miles per hour. A sports car passes the first patrol car traveling at 60 miles per hour; then 5 minutes later, it passes the second patrol car going 65 miles per hour. Analyze this situation to show that at some time between the two clockings, the sports car exceeded the speed limit. Hint: Use the MVT. 1926 1939 10,000 Source: www.biologycorner.com/worksheets/kaibab.html a. Estimate P'(t) for 1905 <t< 1939. b. Graph and interpret P'(t). 47. In 1913, Carlson studied a growing culture of yeast (see Problem 45 in Problem Set 2.4 and Section 6.1). The table of population densities N(t) at one-hour intervals is shown here: 50. Suppose two race cars begin at the same time and finish at the same time. Analyze this situation to show that at some point in the race they had the same speed. Time Population Time Population Time Population 9.6 6. 174.6 12 594.8 1 18.3 7 257.3 13 629.4 20.0 250 7 14 640 8
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