Question

The number of bactena in a refigerated food product is given by N(T)=23T²-44T+16, 2 where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T(t)=9t+1.2, whece t is the time in hours. Find the composite function N(T(t)) : N(T(t))

Answer 1

The composite function N(T(t)) is 1872t² + 100t - 3.68.

Step-by-step explanation:

To find the composite function N(T(t)), we substitute T(t) into N(T) and simplify the expression. First, substitute T(t) = 9t + 1.2 into N(T):

N(T(t)) = 23(9t + 1.2)² - 44(9t + 1.2) + 16

Next, simplify the expression:

N(T(t)) = 23(81t² + 21.6t + 1.44) - 44(9t + 1.2) + 16

N(T(t)) = 1872t² + 496.8t + 33.12 - 396t - 52.8 + 16

N(T(t)) = 1872t² + 100t - 3.68

So, the composite function N(T(t)) is given by N(T(t)) = 1872t² + 100t - 3.68.