# Calculus (Derivatives)

A tray of lasagna comes out of the oven at 200°F and is placed on a table where the surrounding room temperature is 70°F. The temperature T (in °F) of the lasagna is given by the function T(t) = e^(4.86753 - t) + 70, where t is time (in hours)after taking the lasagna out of the oven. t is greater than or equal to 0.
At which of the following times is the lasagna cooling SLOWEST?

A. 3 hours after being taken out of the oven
B. 5 hours after being taken out of the oven
C. 6 hours after being taken out of the oven
D. 7 hours after being taken out of the oven
E. 9 hours after being taken out of the oven

I want to say that it is E. 9 hours after being taken out of the oven, but I am a little unsure. Any help is appreciated!

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1. subbing in the time will give you the temperature.
e.g. I will do B
T(5) = e^(4.86753-5) + 70
= 70.88°

and for E:
T(9) = e^(4.85753-9) + 70 = 70.016°

Your last question deals with the "rate of change"
You can use common sense or intuition to tell that the slowest change would happen at 9 hrs

To find exact answers, take the derivative of your equation, and sub in the different values.

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