Question

The number of bacteria in a refrigerated food product is given by N(T) = 24T^2 - 91 T + 65, for 3 < T < 33. The variable T is the temperature of thefood.When the food is removed from the refrigerator, the temperature is given byT(t) = 3 t + 1.6 , where t is the time in hours.Find the composite function N(T(t)):

Answer 1

Answer:

The answer to your question is

Step-by-step explanation:

               N(T)  = 24T² - 91 T + 65         and T(t) = 3t + 1.6

         N(T(t)) = 24(3t + 1.6)² - 91(3t - 1.6) + 65

         N(T(t)) = 24 (9t² + 9.6t + 2.56) - 273t - 145.6t + 65

        N(T(t)) = 216t² + 230.4t + 61.44 - 273t - 145.6 + 65

        N(T(t)) = 216t² - 42.6t - 9.16

Answer 2

The composite function $N(T(t))=216t^2-42.6t-19.16$

What is a function?

• "It defines the relation between input and output values."
• "In function, for each input there is exactly one output."

What is composition of function?

"It is an operation between two functions such that the output of one function is the input of the other."

For given question,

we have been given two functions $N(T) = 24T^2 - 91 T + 65$ for 3 < T < 33 and $T(t) = 3 t + 1.6$

where function N(T) represents the number of bacteria in a refrigerated food product

and function T(t) represents the temperature of the food

We need to find the composite function N(T(t))

$N(T(t))\\\\=N(3 t + 1.6)\\\\= 24(3 t + 1.6)^2 - 91 (3 t + 1.6) + 65\\\\= 24(9t^2+9.6t+2.56)-273t-145.6+65\\\\=216t^2+230.4t+61.44-273t-80.6\\\\=216t^2-42.6t-19.16$

Therefore, the composite function $N(T(t))=216t^2-42.6t-19.16$

Learn more about the composite function here:

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