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
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...
Related questions
Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4db1e84-75df-498d-9686-5cabfd0e0c2f%2Fc75fe91a-66b8-48bd-8b71-104576e3b922%2F4s5p0s_processed.jpeg&w=3840&q=75)
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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