Chapter 8.8, Problem 4CCYP

To determine

Find the maximum population of fishes in the lake.

Answer to Problem 4CCYP

  $1880$

Explanation of Solution

Given information:

The population of a certain species of fish in a lake after $\mathrm{t}$ years be modelled by the function

  $\mathrm{P}\left(\mathrm{t}\right)=\frac{1880}{1+1.42{\mathrm{e}}^{-0.037\mathrm{t}}}$ , where $\mathrm{t}\ge 0$

Calculation:

Consider, the function,

  $\mathrm{P}\left(\mathrm{t}\right)=\frac{1880}{1+1.42{\mathrm{e}}^{-0.037\mathrm{t}}}$

Graph the function for $0\le \mathrm{t}\le 500$ .

  

As per the graph the $\mathrm{y}-\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}$ approaching $1880$ .so the maximum population is $1880$ ,

Hence the maximum population is $1880$ .