7. While on the road trip, Prolific's rental car's engine overheats, and he pulls over on the
highway to allow it to cool. The outside temperature is 71°F. After 98 seconds, the temperature
of the engine is 233°F. The temperature T, of the surface of a given engine after it has been
cooling for t minutes can best be modeled by the function below, where T. is the temperature
of the room and k is a constant.
In (T-T.)=-kt +4.718
A. Compute the value of k to the nearest hundredth.
B. Using this value of k, find the temperature T, of the engine that has been resting for a
total of 212 seconds. Express your answer to the nearest degree.
C. Engines operate safely between 190°F and 220°F. Determine if Prolific's car is safe to
drive after 3 minutes of waiting.
