Assume that y = y(t) satisfies the logistic equation withy0 = y(0) the initial value of

Chapter 8, Problem 49

(choose chapter or problem)

Assume that $y=y(t)$ satisfies the logistic equation with $y_{0}=y(0)$ the initial value of y

(a) Use separation of variables to derive the solution

$y=\frac{y_{0} L}{y_{0}+\left(L-y_{0}\right) e^{-k t}}$

(b) Use part (a) to show that $\lim _{t \rightarrow+\infty} y(t)=L$.

Equation Transcription:

$y=y(t)$

${y}_{0}=y(0)$

$y=\frac{{y}_{0}L}{{y}_{0}+\left({L-{y}_{0}}\right){e}^{-kt}}$

${lim}_{t\rightarrow{}+\infty{}}\ y(t)=L$

Text Transcription:

y=y(t)

y_0=y(0)

y=y_0L/y_0+L-y_0e^-kt

lim_t rightarrow +infinity y(t)=L

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