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The number of bacteria in a refrigerated food product is given by N(T) = 26T2 - 123T + 25,

5
When the food is removed from the refrigerator, the temperature is given by T(t) = 4t + 1.2 , where t is

the time in hours.

Find the composite function N(T()):

N(T()) 26( T - t)2 – 123(1)

syntax error.

Find the time when the bacteria count reaches 16044. Give your answer accurate to at least 2 decimal

places.

Time Needed = 10845768.99233358

hours

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MrRoyal

Answer:

(A)

N(T(t)) = 416t² - 242.4 - 135.16

(B)

Time = 27.30 hours

Step-by-step explanation:

Given

N(T) = 26T² - 123T + 25

T(t) = 4t + 1.2

Solving for the composite function.

Substitute T for 4t + 1.2 in N(T)

N(T(t)) = 26(4t + 1.2)² - 123(4t + 1.2) + 25

N(T(t)) = 26(4t+1.2)(4t + 1.2) - 123(4t + 1.2) + 25

N(T(t)) = 26(16t² + 9.6t + 1.44) - 492t - 147.6 + 25

N(T(t)) = 416t² + 249.6t + 37.44 - 492t - 172.6

N(T(t)) = 416t² + 249.6t - 492t + 37.44 - 172.6

N(T(t)) = 416t² - 242.4 - 135.16

Solving for time.

We have that

N(T) = 16044

N(T) = 26T² - 123T + 25

This gives

16044 = 26T² - 123T + 25

26T² - 123T + 25 - 16044 = 0

26T² - 123T - 16019 = 0

Solve by quadratic, we have.

T = 27.299506396472

Or

T = -22.568737165703

Since time can't be negative

T = 27.299506396472

T = 27.30 (approximately)

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