Please do both part A and B Under certain conditions, the number of diseased cells $N(t)$ at time $t$ increases at a rate $N^{\text{'}}(t)=A{e}^{kt},$ where $A$ is the rate of increase at time $0($in cells per day$)$ and k is a constant.

a$.$ Suppose $A=60,$ and at $5$ days, the cells are growing at a rate of $180$ per day. Find a formula for the number of cells after $t$ days, given that $200$ cells are present at $t=0.$

b$.$ Use your answer from part a to find the number of cells present after $14$ days.

a$.$ Find a formula for the number of cells, $N(t),$ after $t$ days.

$N(t)=$

$$

$($Round any numbers in exponents to five decimal places. Round all other numbers to the nearest tenth.$)$