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logistics equation limiting factor...i dont get it

MrDudeMan

Lifer
i am working on a differential equations homework problem and ive been trying to figure this out for some time now.

the problem states how many people will be infected, with given initial conditions and a maximum value of 50,000. my problem is i dont understand what equation to incorporate into this problem to use the 50,000.

i solved the logistics equation and got the general form, but now im stuck because i dont know how to use the 50,000. anybody?

my best guess so far is P = a/2b, where a and b are stated in the logistics equation.
 
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