Calculus (Derivatives)
posted by Mishaka on .
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!

subbing in the time will give you the temperature.
e.g. I will do B
T(5) = e^(4.867535) + 70
= 70.88°
and for E:
T(9) = e^(4.857539) + 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.