We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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.

vest4R Mar 29, 2018