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)) :

Question

Suarez

Mathematics

20 September, 09:30

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)) :

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Answers (1)

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Maleah Fitzpatrick · Answer 1

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