+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 still get quite complex and I'm not sure If I've done it correctly.
Thank you.
