I have the equation:


this equation was derived from solving the logistic growth equation:



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.

vest4R  Mar 30, 2018

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:


Alan  Mar 30, 2018

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?

vest4R  Mar 30, 2018


It's blocked for me as well!


However, if you scroll through the Answers pages (try https://web2.0calc.com/answers/page/8179) you can see the image.  It's only when you select the specific question (or answer) that the image is blocked!  

Alan  Mar 31, 2018

great! thank you. yes I got the same with:

vest4R  Mar 31, 2018

6 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.