In Problems 11–20, the given logistic differential equation models the rate of change of a population P with respect to time t. For each differential equation, find (a) the carrying capacity M. (6) the maximum population growth rate k. C) the population when P is growing most rapidly. (a (E dP dP 11. = 0.12P dt 12. =0.03 P 1- %3D 1 1000 dt 570 33. S d P 14. dt PAGE dP 13, = 0.25 P dt 0.08P 563 1600 4000 P dP 15. = 0.002P dt d P 16. = 0.005 P (1 15,000 1 2800 dt
In Problems 11–20, the given logistic differential equation models the rate of change of a population P with respect to time t. For each differential equation, find (a) the carrying capacity M. (6) the maximum population growth rate k. C) the population when P is growing most rapidly. (a (E dP dP 11. = 0.12P dt 12. =0.03 P 1- %3D 1 1000 dt 570 33. S d P 14. dt PAGE dP 13, = 0.25 P dt 0.08P 563 1600 4000 P dP 15. = 0.002P dt d P 16. = 0.005 P (1 15,000 1 2800 dt
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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Transcribed Image Text:In Problems 11–20, the given logistic differential equation models the
rate of change of a population P with respect to time t. For each
differential equation, find
W
(a) the carrying capacity M.
(b) the maximum population growth rate k.
l©) the population when P is growing most rapidly.
(a
(E
dP
P
dP
P
11.
= 0.12P
dt
= 0.03P 1
12.
%3D
1000
dt
570
dP
13.
= 0.25P 1
dt
dP
PAGE
14.
= 0.08 P ( 1
563
33. S
%3D
4000
dt
1600
dP
15.
0.002P
dt
d P
P.
1.
2800
16.
= 1
0.005P
dt
15,000
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