population and rate of growth (logistic function)

lynn005

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Joined
Mar 19, 2007
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7
I am terrible of word problems and have tried numereous times to figure it out and have failed. Here is the proplem:

Given the logistic function with k = 0.0001 and t in years, assume that there are 400 units initially and that the maximum population size is 5200. Find the growth function G(t) and the population and rate growth of population for 1 and 4 years.

Thanks.
Jen
 
Is this a differential equations problem where the initial condition is
P(0)=400?
 
Yes this is a differential word problem with the inital 400 but not to exceed 5200. Thanks.
Jen
 
logistic rate of change is a joint proportion ...

\(\displaystyle \L \frac{dy}{dt} = ky(M-y)\)
 
I figure out to get the population rate you use the formula
G(t)= 5200/1+ 12e^-0.52t
to solve for 1 and 4 years you stick the 1,4=t in the problem, but I can't figure out how to find the rate of growth given that k=0.0001, 400 intial population and 5200 maximum size. Thanks.
Jen
 
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