$3700$ people live in Pleasant$-$Ville. One person contracts a particularly contagious strain of influenza. No

one in Pleasant$-$Ville has been vaccinated, so all are susceptible.

The spread of the disease in the community is modeled by:

$A=\frac{3700}{1+3699e^{-0\mathrm{.}6t}}$

where $A$ is the number of people who have contracted the flu after $t$ days.

Round all answers to a whole number.

$($a$)$ Determine the number of people who have contracted the flu after $7$ days:

$($b$)$ Determine the carrying capacity for this model:

$($c$)$ Determine the number of days that it will take for $275$ people to contract the flu: