Suppose a certain population obeys the logistic equation dy dt = ry[1 − (y/k)]. (a) if y0 = k/3, find the time τ at which the initial population has doubled. find the value of τ corresponding to r = 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 and β = 0.9.