Question

The number of bacteria (b) in a batch of refrigerated food is given by the function b(t) = 20t2 − 70t + 300, where t is the temperature of the food in degrees Fahrenheit. The function t(h) = 2h + 3 gives the temperature of the food h hours after it is removed from refrigeration. Which expression correctly represents the number of bacteria (b) in the food as a function of the number of hours (h) the food is unrefrigerated?

Answer 1

If the number of bacteria $b(t)$ is a function only of temperature $t$, and the temperature $t(h)$ is a function only of time in hours $h$, then

$b(t(h))=b(2h+3)=20(2h+3)^4-70(2h+3)+300$
$b(t(h))=320h^4+1920h^3+4320h^2+4180h+1710$