Question

A herd of 23 white-tailed deer is introduced to a coastal island where there had been no deer before. Their population is predicted to increase according to A=276/1+11e^(- .35t)where A is the number of deer expected in the herd after t years.(a) How many deer will be present after 3 years? Round your answer to the nearest whole number.(b) How many years will it take for the herd to grow to 50 deer? Round your answer to the nearest whole number.

Answer 1

Given:

`A=(276)/(1+11e^(-0.35t))`

Where A is the number of deer expected in the herd after t years.

We will find the following:

(a) How many deer will be present after 3 years?

So, substitute t = 3 into the given equation:

`A=(276)/(1+11e^(-.35*3))\approx56.9152`

Rounding to the nearest whole number

So, the answer will be A = 57

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(b) How many years will it take for the herd to grow to 50 deer?

substitute A = 50 then solve for t

`\begin{gathered} 50=(276)/(1+11e^(-.35t)) \\ 1+11e^(-.35t)=(276)/(50) \\ \\ 11e^(-.35t)=(276)/(50)-1=4.52 \\ e^(-.35t)=(4.52)/(11) \\ -0.35t=ln((4.52)/(11)) \\ \\ t=(ln((4.52)/(11)_))/(-0.35)=2.54 \end{gathered}`

Round your answer to the nearest whole number.

So, the answer will be t = 3