Population growth according to logistic law

Question

I am working on HomeWork problem from differential equation by Martin Braun.

A population grows according to the logistic 1aw, with a limiting population of 5 X 10^8 individuals. When the population is low, it doubles every 40 minutes. What will the population be after two hours if initially, it is 10^8?

We have the closed form of the population. How the growth when the population is low different from it?

Braun Book page number-37 problem -6

https://mcdtu.files.wordpress.com/2017/03/texts-in-applied-mathematics-11-martin-braun-auth-differential-equations-and-their-applications_-an-introduction-to-applied-mathematics-springer-new-york-1993.pdf