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CalculusQ&A LibrarySuppose that 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.Start your trial now! First week only $4.99!*arrow_forward*

Question

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

a.If *y*_{0} = *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 *y*_{0}/*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.

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