
Continuous Model
This is actually a problem for my calculus class but it's mostly diff. eq.
Given I'(t)=aI(NI) with the initial condition I(0)=1
solve this equation and show that the solution can be written as:
I(t)=N/(1+Be^(aNt))
any help would be greatly appreciated.

$\displaystyle \frac{dI}{dt}$ = $\displaystyle aI(NI)$
$\displaystyle \frac{dI}{aI(NI)}$ = $\displaystyle dt$
Try to find
$\displaystyle \frac{1}{aI(NI)}$ = $\displaystyle \frac{z1}{aI}$ + $\displaystyle \frac{z2}{NI}$.
Find z1 and z2.
Integration give left side will be two functions ln, right t+C.

so it looks like I'm to use fractional decomposition. Which Still has me stumped.