Suppose that the population of deer on an island is modeledby the equationP (t) = 955

Chapter 3, Problem 51

(choose chapter or problem)

Suppose that the population of deer on an island is modeled by the equation

$P(t)=\frac{95}{5-4 e^{-1 / 4}}$

where $P(t)$ is the number of deer t weeks after an initial observation at time $t=0$.

(a) Use a graphing utility to graph the function $P(t)$.

(b) In words, explain what happens to the population over time. Check your conclusion by finding $\lim _{x \rightarrow+\infty} P(t)$

(c) In words, what happens to the rate of population growth over time? Check your conclusion by graphing $P^{\prime}(t)$

Equation Transcription:

$P(t)=\frac{95}{5-4{e}^{-t/4}}$

$P(t)$

$t=0$

$\lim\limits_{{x} \rightarrow {+\infty{}}}P(t)$

${P}^{'}(t)$

Text Transcription:

P(t)=95/5-4e^-t/4

P(t)

t=0

lim_x rightarrow + inifinity P(t)

P'(t)

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