dy dt =r(t)y-k, 1 + sint r(t) = y(0) = yo, where the growth rate r(t) is given by and k represents the rate of predation. 9 7 1 a) Suppose that k = Select the figure that represents y versus t 7 for yo 0.5, 0.75, 1. Figure 3 W b) Estimate the critical initial population y, below which the population will become extinct. NOTE: Round your answer to two decimal places. Ye= 0.75 c) Find a general relation between k and the corresponding e then plot ye versus k. There is a linear dependence of ye on k. ✓ X 1 Ve X
dy dt =r(t)y-k, 1 + sint r(t) = y(0) = yo, where the growth rate r(t) is given by and k represents the rate of predation. 9 7 1 a) Suppose that k = Select the figure that represents y versus t 7 for yo 0.5, 0.75, 1. Figure 3 W b) Estimate the critical initial population y, below which the population will become extinct. NOTE: Round your answer to two decimal places. Ye= 0.75 c) Find a general relation between k and the corresponding e then plot ye versus k. There is a linear dependence of ye on k. ✓ X 1 Ve X
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
Question
Transcribed Image Text:Suppose that a certain population satisfies the initial value problem
dy
=
= r(t)y-k, y(0) = 30, where the growth rate r(t) is given by
dt
1+ sint
r(t) =
9
7
and k represents the rate of predation.
a) Suppose that k =
for yo 0.5, 0.75, 1.
Figure 3
Ye=0.75
Select the figure that represents y versus t
b) Estimate the critical initial population y, below which the
population will become extinct.
NOTE: Round your answer to two decimal places.
c) Find a general relation between
k and the corresponding ye
then plot ye versus k.
There is a linear
dependence of ye on k. ✓
X
Ve
V
X
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
