Problem 1: A biologist friend has spent the past 25 months tracking the populations of two different species of fish. Let A(t) and B(t) be the size of each fish population t months after her observations began. While looking through her research journal, you find the following information: A"(t) 10 15 20 25 A' (10) = A'(20) = 0 -5 jotted down along with the graph of A"(t) shown to the right. --10 (a) When was the rate of change of the fish A population increasing? When was it decreasing? (b) When was the size of the fish A population increasing? When was it decreasing? (c) Which is bigger, the average rate of change in the fish A population between month 0 and month 5 or the average rate of change in the population between month 5 and month 10? (d) One of the results of your friend's research is that the size of the two fish populations are related. In particular, she notes that B(t) = 0.5A(t) +t² – 10t – 100. Which of the following statements was true about the fish B population at time t = 10: (i) After ten months, the fish B population was growing and the growth was speeding up. (ii) After ten months, the fish B population was growing and the growth was slowing down. (iii) After ten months, the fish B population was declining and the decline was speeding up. (iv) After ten months, the fish B population was declining and the decline was slowing down.
Problem 1: A biologist friend has spent the past 25 months tracking the populations of two different species of fish. Let A(t) and B(t) be the size of each fish population t months after her observations began. While looking through her research journal, you find the following information: A"(t) 10 15 20 25 A' (10) = A'(20) = 0 -5 jotted down along with the graph of A"(t) shown to the right. --10 (a) When was the rate of change of the fish A population increasing? When was it decreasing? (b) When was the size of the fish A population increasing? When was it decreasing? (c) Which is bigger, the average rate of change in the fish A population between month 0 and month 5 or the average rate of change in the population between month 5 and month 10? (d) One of the results of your friend's research is that the size of the two fish populations are related. In particular, she notes that B(t) = 0.5A(t) +t² – 10t – 100. Which of the following statements was true about the fish B population at time t = 10: (i) After ten months, the fish B population was growing and the growth was speeding up. (ii) After ten months, the fish B population was growing and the growth was slowing down. (iii) After ten months, the fish B population was declining and the decline was speeding up. (iv) After ten months, the fish B population was declining and the decline was slowing down.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem 1:
A biologist friend has spent the past 25 months
tracking the populations of two different species
of fish. Let A(t) and B(t) be the size of each fish
population t months after her observations began.
While looking through her research journal, you
find the following information:
A" (t)
10
15
20
25
A'(10) = A'(20) = 0
%3D
jotted down along with the graph of A"(t) shown
to the right.
--10
(a) When was the rate of change of the fish A population increasing? When was it decreasing?
(b) When was the size of the fish A population increasing? When was it decreasing?
(c) Which is bigger, the average rate of change in the fish A population between month 0 and
month 5 or the average rate of change in the population between month 5 and month 10?
(d) One of the results of your friend's research is that the size of the two fish populations are
related. In particular, she notes that
B(t) = 0.5A(t) +t² – 10t – 100.
Which of the following statements was true about the fish B population at time t = 10:
(i) After ten months, the fish B population was growing and the growth was speeding up.
(ii) After ten months, the fish B population was growing and the growth was slowing down.
(iii) After ten months, the fish B population was declining and the decline was speeding up.
(iv) After ten months, the fish B population was declining and the decline was slowing down.
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