suppose that a certain population obeys the logistic equation dy/dt=ry[1−(y/K)].

(a) If y0=K/3,find the timeτat which the initial population has doubled. Find the value of τ corresponding tor=0.025 per year.

(b) If y0/K=α, find the time T at which y(T)/K=β, where 0<α,β<1. Observe that T→∞ as α→0 or as β→1. Find the value of T for r=0.025 per year,α=0.1, andβ=0.9.