Composition of Functions · Exercise 102

The number of bacteria in a refrigerated food product is given by $N\left(T\right)=23T^2-56T+1,$ $3<T<33,$ where $T$ is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by $T\left(t\right)=5t+1.5,$ where $t$ is the time in hours.

ⓐFind the composite function $N\left(T\left(t\right)\right).$
ⓑFind the time (round to two decimal places) when the bacteria count reaches 6752.

OpenStax, Algebra and Trigonometry 2e · §3.4 Composition of Functions · Exercise 102