A bottle of white wine at room temperature (68°F) is placed in a refrigerator at 3 P.M. Its temperature after t hours is changing at the rate of -18e^-0.6^t°F/hr.
By how many degrees will the temperature of the wine have dropped by 12 P.M.? Please round your answer to one decimal place.

Question

Quizplus · Accepted Answer

To find the temperature drop by 12 P.M., we calculate the change in temperature from 3 P.M. to 12 P.M., which is 9 hours. The rate of temperature change is given by the function -18e^(-0.6t). To find the total change, we integrate this rate from 0 to 9 hours:$$\int_{0}^{9} -18e^{-0.6t} \, dt$$This gives us the total change in temperature over the 9 hours. Performing this calculation, we find that the temperature of the wine drops by approximately 29.9°F by 12 P.M.

A Bottle of White Wine at Room Temperature (68°F) Is