Question

The number of bacteria in a refrigerated food product is given by N(T) = 27T^2 - 155T + 66, 6 < T < 36, where T is the temperature of the food.When the Food is removed from the refrigerator, the tempersture is given by T(t) = 6t + 1.7, where t is the time in hours.Find the composite function N(T(t)): N(T(t)) =Find the time when the bacteria count reaches 26087. Time needed = ____ hours

Answer 1

The composite function is N(T(t))) = 972t² + -379.2t + 407.53 and the time taken is 5.41 seconds

How to evaluate the composite function

From the question, we have the following parameters that can be used in our computation:

N(T) = 27T² - 155T + 66

Also, we have

T(t) = 6t + 1.7

The composite function (N(T(t)) is calculated as

N(T(t))) = 27T(t))² - 155T(t)) + 66

Substitute the known values into the equation

N(T(t))) = 27(6t + 1.7)² - 155(6t + 1.7) + 66

This gives

N(T(t))) = 972t² + -379.2t + 407.53

When the bacteria reached 26807, we have

972t² + -379.2t + 407.53 = 26807

This gives

972t² + -379.2t - 26399.47 = 0

Solving graphically, we have

t = 5.41

Hence, the time taken is 5.41 seconds

Answer 2

Okay, here we have this:

Considering the provided information, we are going to calculate the requested composition and time, so we obtain the following:

Composite function N(T(t)):

`\begin{gathered} N(6t+1.7)=27\mleft(6t+1.7\mright)^2-155\mleft(6t+1.7\mright)+66 \\ =27\mleft(36t^2+20.4t+2.89\mright)-155\mleft(6t+1.7\mright)+66 \\ =972t^2+550.8t+78.03-155\mleft(6t+1.7\mright)+66 \\ =972t^2-379.2t-119.47 \end{gathered}`

Finally we obtain that N(T(t)) is equal to 972t^2-379.2t-119.47.

Now, let's the time when the bacterias count reaches 26087: