Find missing coefficients - calculus

Question

Let f(t)=a/(1+be^(.9t)), modeling cell growth. At t=0, the population is 20 and is increasing at 16 cells an hour.

Find a and b.

Answer 1

f(0) = a / (1 + b )

20 = a / (1 + b)

20(1 + b) = a

f(1) = a / (1 + be^0.9)

36 = a / (1 + be^0.9)

36(1 + be^0.9) = a

Both left sides are equal to a. They are equal to each other. Solve for b, then for a.