Question

The number of bacteria in a refrigerated food product is given by N ( T ) = 27 T 2 − 180 T + 100 N(T)=27T2-180T+100, 7 < T &lt; 37 7

Answer 1

Answer:

$N(T(t))=432t^2-374.4t-118.88$

The number of Bactria after 5.8 hours is 12242.

Step-by-step explanation:

The number of bacteria in a refrigerated food product is given by

$N(T)=27T^2-180T+100$

where, T is the temperature of the food.

When the food is removed from the refrigerator, then the temperature is given by

$T(t)=4t+1.6$

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

$N(T(t))=N(4t+1.6)$

$N(T(t))=27(4t+1.6)^2-180(4t+1.6)+100$

$N(T(t))=432t^2+345.6t+69.12-720t-288+100$

$N(T(t))=432t^2-374.4t-118.88$

where N(T(t)) is the number of bacteria after t hours.

Substitute t=5.8 in the above function.

$N(T(5.8))=432(5.8)^2-374.4(5.8)-118.88$

$N(T(5.8))=14532.48-2290.4$

$N(T(5.8))=12242.08$

$N(T(5.8))\approx 12242$

Therefore, the number of Bactria after 5.8 hours is 12242.