$2.$ Consider a population with the following characteristics; initial biomass of $50$ mg$/$L$,$maximum specific growth rate of $1\mathrm{.}2$ day$-1$ and a decay rate coefficient of $0\mathrm{.}05$ day$^-1.$

$($a$)$ Assume logistic growth and calculate the population$$s biomass after $1,2,5,10,$ and $20$

days if the carrying capacity is $5000$ mg$/$L$.$

$($b$)$ Assume exponential growth to calculate the population biomass for the same time

points.

$($c$)$ At approximately what time do the two models begin to obviously deviate?

$($d$)$ What percent of the population of the exponential growth model at $10$ days is equal to

the carrying capacity?