The growth of a certain type of weed satisfies a differential equation of the following form.

dy/dt=ky(a-y)

A typical weed has length 7 centimeters after 8 days, length 42 centimeters after 22 days, and reaches length 48 centimeters at maturity. Find a formula foryas a function of time,t. (Enter all numerical values in your equation correct to at least four decimal places.)