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

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:

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