+251 I have the equation:
\(P(t)=\frac{K}{9e^{-rt}+1}\)
this equation was derived from solving the logistic growth equation:
\(\frac{dP}{dt}=rP\big(1-\frac{P}{K}\big)\)
where,
r is the rate of growth = 1.13
K is the maximum population = 10,000
I've been asked to change the growth rate to:
\(r= 0.83 + \frac{0.3}{1+0.3t}\)
My question is,
Do I have to solve the entire logistic growth equation again, that is,
or can I just substituted r into the derived equation and rearrage, that is,
I wanted to get some clarification as I've tried doing both process with a simpler equation, however the answer I get quite is complex and I'm not sure If I've done it correctly.
In my opinion I don't think it matters if I substitute the new r straight into P(t) ... but i'm not overly confident about that
Thank you.
+33615 I don't see how you can avoid doing the integration again, since r is now a function of t. The result I get when so doing is as follows:
+251 thanks for your reply Alan. I was thinking that might be the case.
I see your image has been blocked. Would you be able to unblock it please?
