Question

The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. The population is modeled by the function n = f(t) = a/(1 + be^−0.5t) where t is measured in hours. At time t = 0 the population is 10 cells and is increasing at a rate of 4 cells/hour. Find the values of a and b.

Answer 1

well, just plug in some numbers!

f(0) = 10, so
a/(1+b) = 10

df/dt = a(0.5be^(-0.5t))/(1+be^-0.5t)^2, so
a(b/2)/(1+b)^2 = 4

Solve those two equations, and you get
a = 50
b = 4

Answer 2

I still don't understand how you got those values for a and b. What was the final step?