Chapter 4.5, Problem 12E

Reminder Round all answers to two decimal places unless otherwise indicated.

Dispersion Model Animal populations move about and disperse. A number of models for this dispersion have been proposed, and many of them involve the logarithm. For example, in $1965$, O.H.Paris released a large number of pill bugs and after $12$ hours recorded the number $n$ of individuals that could be found within $r$ meters from the point of release. He reported that the most satisfactory model for this dispersion was

$n=-0.772+0.297\log r+\frac{6.991}{r}$.

a. Make a graph of $n$ versus $r$ for the circle around the release point with the radius $15$ meters.

b. How many pill bugs were to be found within $2$ meters from the release point?

c. How far from the release point would you expect to find only a single individual?