We want to combine b(t) and t(h) to create a function that described the number of bacteria, b, as a function of time, h.
This function can be called b(t(h)), or b(h).
Consider the function b(t), or bacteria as a function of temperature.
b(t) = 20t² - 70t +300
This describes the number of bacteria, given the temperature.
t(h) described the temperature as a function of time, specifically hours after refrigeration:
t(h) = 2h + 3
Since the time h can tell us the temperature t, and the temperature t can tell us the # of bacteria b, we can create a function that tells us the number of bacteria, b, given hours following refrigeration, h.
To do this, we plug t(h) in for every t in the b(t) function:
b(t(h)) = 20 (2h+3)² - 70(2h+3) + 300
We can also call this function b(h), since we now can express b as a function of h.
Simplify the function:
b(h) = 20 (4h²+12h+9)-14h-210+300
b(h) = 80h² +100h +270
The Answer is B
