Chapter 2.6, Problem 7E

Marine Fishery One class of models for population growth rates in marine fisheries assumes that the harvest from fishing is proportional to the population size. For one such model, we have

$G=0.3n\left(1-\frac{n}{2}\right)-0.1n$

Here G is the growth rate of the population, in millions of tons of fish per year, and n is the population size, in millions of tons of fish.

a. Make a graph of G versus n. include values of n up to 1.5 million tons.

b. Use functional notation to express the growth rate if the population size is 0.24 million tons, and then calculate that value.

c. Calculate $G\left(1.42\right)$ and explain in practical terms what your answer means.

d. At what population size is the growth rate the largest?