The function $p(t)=\frac{2000t}{4t75}$ gives the population $p$ of deer in an area after $t$ months.

a$)$ Find $p^{\text{'}}(16),p^{\text{'}}(80),$ and $p^{\text{'}}(160).$

b$)$ Find $p^{\text{'}\text{'}}(16),p^{\text{'}\text{'}}(80),$ and $p^{\text{'}\text{'}}(160).$

c$)$ Interpret the meaning of your answers to part $($a$)$ and $($b$).$ What is happening to the population of deer in the long term?

a$)p^{\text{'}}(16)={7\mathrm{.}764}^{**}$ deer $\frac{?}{?}$ month $.$

$($Type an integer or decimal rounded to three decimal places as needed.$)$

$p^{\text{'}}(80)=$

$$

$($Type an integer or decimal rounded to three decimal places as needed.$)$