Consider the following population model

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3. Consider the following population model
dN
N
0.02 N(1 –
100
N(0) = 100
dt
(a) Show that the differential equation can be written in the form
dN
= -k((N – A)² + B)
dt
where k, A, B are positive constants.
(b) Solve the initial value problem.
(c) Determine the time that the population extincts (N(T) = 0). Round your answer to one
decimal place.
Transcribed Image Text:3. Consider the following population model dN N 0.02 N(1 – 100 N(0) = 100 dt (a) Show that the differential equation can be written in the form dN = -k((N – A)² + B) dt where k, A, B are positive constants. (b) Solve the initial value problem. (c) Determine the time that the population extincts (N(T) = 0). Round your answer to one decimal place.
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