F$.$ E$.$ Smith has studied population growth for the water flea. Let N denote the population size. In one experiment, Smith found that G$,$ the rate of growth per day in the population, can be modeled by the following function.

G $=$

$0\mathrm{.}44$N$(228$ N$)228+3\mathrm{.}46$N

$$

$($a$)$ Draw a graph of G versus N$.$ Include values of N up to $350.$

$($b$)$ At what population size does the greatest rate of growth occur? $($Round your answer to the nearest whole number.$)$

fleas

$($c$)$ There are two values of N where G is zero. Find these values of N$.$

fleas $($smaller value$)$fleas $($larger value$)$

Explain what is occurring at the smaller population level.

The size of the population is not changing.The size of the population is growing.$$The size of the population is shrinking.

Explain what is occurring at the larger population level.

The size of the population is not changing.The size of the population is growing.$$The size of the population is shrinking.

$($d$)$ What is the rate of population growth if the population size is $290?($Round your answer to two decimal places.$)$

fleas per day

Explain what is happening to the population at this level.

At this level, the population is decreasing.At this level, the population is increasing.$$At this level, the growth rate is increasing.At this level, the growth rate is not changing.