# population growth using ODE's

by cheddacheeze
Tags: growth, ode, population
 P: 42 does the equation become just for the subtitution $\frac{-1}{ln(1000-P)}$
 HW Helper P: 1,495 No. It appears that you do not know how to integrate by substitution. Looking at the problem you have presented you ought to have followed a course at some point that taught you how to do it. I suggest reviewing the basics of integration before continuing with this problem.
 P: 42 $\frac{1}{5} lnP - \frac{1}{5} ln(1000-P)= t+C$ $lnP - ln(1000-P) = 5t+5c$ using log rules $ln \frac{P}{1000-P} = 5t+5c$ multiplying by e $\frac{P}{1000-P}=Ae^{5t} , A=e^{5c}$ $P = (1000-P)(Ae^{5t})$ multiplying it out $P=1000Ae^{5t} - PAe^{5t}$ $P + PAe^{5t} = 1000Ae^{5t}$ $Ae^{5t}= 1000Ae^{5t}/P$ $P = 1000$ but how do i get P(t)
 P: 42 turns out i just had to use rearranging to find my P(t)

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