Question

A tray of lasagna comes out of the oven at 200 F and is placed on a table where the surrounding temperature is 70 degrees F. The temperature T (in Fahrenheit) of the lasagna is given by the function T(t)=70+e^(4.86753-t), 0< t where t is time(in hours) after taking the lasagna out of the oven.

What is the rate of change in the temperature of the lasagna exactly two hours after taking it out of the oven?

Answer 1

The rate of change in the temperature of the lasagna exactly two hours after taking it out of the oven is approximately -2.289 degrees Fahrenheit per hour.

Step-by-step explanation:

The rate of change in the temperature of the lasagna can be found by taking the derivative of the temperature function with respect to time. In this case, the temperature function is T(t) = 70 + e^(4.86753-t). To find the derivative, we can use the chain rule:

dT/dt = -e^(4.86753-t)

Now, we can evaluate the rate of change at t = 2. Substitute t = 2 into the derivative to find the rate of change at that time:

dT/dt = -e^(4.86753-2)

Using a calculator, we can find that the rate of change in the temperature of the lasagna exactly two hours after taking it out of the oven is approximately -2.289 degrees Fahrenheit per hour.