The temperature on a certain day as measured at the airport of a city is changing at the rate of , where is measured in hours, with corresponding to 6 a.m.The temperature at 6 a.m.was .What was the temperature at 9 a.m.? Please round your answer to whole degrees.

Question

The temperature on a certain day as measured at the airport of a city is changing at the rate of   , where  is measured in hours, with  corresponding to 6 a.m.The temperature at 6 a.m.was  .What was the temperature at 9 a.m.? Please round your answer to whole degrees.

Quizplus · Accepted Answer

The temperature is changing at the rate of $11e^{-12t}$, where $t$ is measured in hours with $t=0$ corresponding to 6 a.m. So, the temperature at time $t$ is given by 
$$T(t) = T_0 + \int_{0}^{t}  11e^{-12s} ds,$$ 
where $T_0$ is the temperature at $t=0$. 
We have $T_0=55$ and $t=3$ (since we want to find the temperature at 9 a.m. which is three hours after 6 a.m.). Thus, 
$$ T(3) = 55 + \int_{0}^{3}  11e^{-12s} ds \approx 65^{\circ} 	ext{F}.$$
Rounding to the nearest whole degree, we get the temperature at 9 a.m. is 65°F. 
Therefore, the answer is (C).

The Temperature on a Certain Day as Measured at the Airport