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

The number of bacteria (b) in the food as a function of the number of hours (h) the food is unrefrigerated can be represented by the expression b(h) = 80h^2 + 160h + 460.

Step-by-step explanation:

To represent the number of bacteria (b) in the food as a function of the number of hours (h) the food is unrefrigerated, we need to use the composition of functions. We can start by plugging in t(h) into the function b(t).

Given that t(h) = 2h + 3, we substitute t(h) into the function b(t) to get:

b(h) = 20(2h + 3)^2 - 70(2h + 3) + 300

We can simplify this expression and expand it to get the final representation of the number of bacteria as a function of hours unrefrigerated: b(h) = 80h^2 + 160h + 460.

Answer 2

1. Collect like terms
20t^2 + (-70 + 300)
2. Simplify
20t^2 + 230