Asked by Erica
Assume that the number of fish P(t) after t years grows according to the logistic equation
dP/dt= P(a-bP) = bP(300 − P)
Find the solution of this DE (with the given initial value at t = 0) as a separable equation. Your solution formula will contain b as an unknown parameter.
I know you use partial fractions, but I get caught up by bP part. I didn't know if you carried it all the way to the end or what...
dP/dt= P(a-bP) = bP(300 − P)
Find the solution of this DE (with the given initial value at t = 0) as a separable equation. Your solution formula will contain b as an unknown parameter.
I know you use partial fractions, but I get caught up by bP part. I didn't know if you carried it all the way to the end or what...
Answers
Answered by
Steve
well, apparently
P(a-bP) = bP(300 − P)
aP - bP^2 = 300bP - bP^2
so, a = 300b
dP/dt = P(300b-bP) = bP(300-P)
Try plugging that in. You already know what the logistic growth function looks like, so that should guide your efforts some.
P(a-bP) = bP(300 − P)
aP - bP^2 = 300bP - bP^2
so, a = 300b
dP/dt = P(300b-bP) = bP(300-P)
Try plugging that in. You already know what the logistic growth function looks like, so that should guide your efforts some.
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