Consider the growth of a population p(t). It starts out with p(0) = A. Suppose the growth is unchecked, and hence p = kp for some constant k. Then p(t) = Of course populations don't grow forever. Let's say there is a stable population size Q that p(t) approaches as time passes. Thus the speed at which the population is growing will approach zero as the population size approaches Q. One way to model this is via the differential equation p = kp(Q- p), p(0) = A. The solution of this initial value problem is p(t) = Hint: Proceed as in the last problem.
Consider the growth of a population p(t). It starts out with p(0) = A. Suppose the growth is unchecked, and hence p = kp for some constant k. Then p(t) = Of course populations don't grow forever. Let's say there is a stable population size Q that p(t) approaches as time passes. Thus the speed at which the population is growing will approach zero as the population size approaches Q. One way to model this is via the differential equation p = kp(Q- p), p(0) = A. The solution of this initial value problem is p(t) = Hint: Proceed as in the last problem.
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:Consider the growth of a population p(t). It starts out with p(0) = A. Suppose the growth is unchecked, and hence
p = kp
for some constant k.
Then p(t) =
Of course populations don't grow forever. Let's say there is a stable population size Q that p(t) approaches as time passes. Thus the speed at which the
population is growing will approach zero as the population size approaches Q. One way to model this is via the differential equation
p = kp(Q - p), p(0) = A.
The solution of this initial value problem is p(t) =
Hint: Proceed as in the last problem.
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