Suppose that a certain population satisfies the initial value problem dy dt 1+ sint = r(t)y – k, y(0) = Y0, where the growth rate r(t) is given by %3D r(t): and k represents the rate of predation. 1 a) Suppose that k = Select the figure that represents y versus t for y = 0.5,0.75, 1. Figure 4 b) Estimate the critical initial population y, below which the population will become extinct. NOTE: Round your answer to two decimal places. Ye =0.6 c) Find a general relation between k and the corresponding y then plot y. versus k. There is a linearv dependence of y, on k.
Suppose that a certain population satisfies the initial value problem dy dt 1+ sint = r(t)y – k, y(0) = Y0, where the growth rate r(t) is given by %3D r(t): and k represents the rate of predation. 1 a) Suppose that k = Select the figure that represents y versus t for y = 0.5,0.75, 1. Figure 4 b) Estimate the critical initial population y, below which the population will become extinct. NOTE: Round your answer to two decimal places. Ye =0.6 c) Find a general relation between k and the corresponding y then plot y. versus k. There is a linearv dependence of y, on k.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
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NEED ANSWER ASAP, NOTE PLEASE DO NOT SKIN ANY PRECEEDING STEPS
![Suppose that a certain population satisfies the initial value problem
dy
r(t)y - k, y(0) = yo, where the growth rate r(t) is given by
dt
1+ sin t
r(t)
and k represents the rate of predation.
%3D
3D
a) Suppose that k =
1
Select the figure that represents y versus t
for yo = 0.5, 0.75, 1.
Figure 4
b) Estimate the critical initial population y, below which the
population will become extinct.
NOTE: Round your ansuer to tuo decimal places.
3D
Ve =0.6
c) Find a general relation between
k and the corresponding yes
then plot y. versus k.
There is a linear
dependence of y. on k.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24958ecd-348a-4805-8fdf-dbaaae7cd76e%2F1f283cba-b3cd-42be-ac2c-96a323d56837%2Fpcomza_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that a certain population satisfies the initial value problem
dy
r(t)y - k, y(0) = yo, where the growth rate r(t) is given by
dt
1+ sin t
r(t)
and k represents the rate of predation.
%3D
3D
a) Suppose that k =
1
Select the figure that represents y versus t
for yo = 0.5, 0.75, 1.
Figure 4
b) Estimate the critical initial population y, below which the
population will become extinct.
NOTE: Round your ansuer to tuo decimal places.
3D
Ve =0.6
c) Find a general relation between
k and the corresponding yes
then plot y. versus k.
There is a linear
dependence of y. on k.
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