Chapter 2.6, Problem 8ECP

The number $N$ of bacteria in a refrigerated food is given by

$N\left(T\right)=8T^2-14T+200,2\le T\le 12$

where $T$ is the temperature of the food in degrees $\text{Celsius}\text{.}$ When the food is removed from refrigeration, the temperature of the food is given by

$T\left(t\right)=2t+2,0\le t\le 5$

where $t$ is the time in hours.

a. Find $(N\circ T)\left(t\right).$

b. Find the time when the bacteria count reaches $1000.$