Chapter 2.6, Problem 62E

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

$N\left(T\right)=10T^2-20T+600,2\le T\le 20$

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

$T\left(t\right)=3t+2,0\le t\le 6$

where $t$ is the time in $\text{hours}\text{.}$

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

(b) Find the bacteria count after $0.5$ hour.

(c) Find the time when the bacteria count reaches $1500.$