Question

Suppose you turn off the engine of your car when the temperature of the engine reaches 190 °F. If the outside temperature is a constant 65 °F, then the temperature T of the engine t minutes after you turn off the engine satisfies the equation below.
ln

T − 65
125

= −0.07t

(a) Solve the equation for T.

(b) Find the temperature of the engine 22 minutes after you turn it off. Give your answer to the nearest tenth of a degree.

Answer 1

\[\ln((T-65)/125)=-0.07t\]

Answer 2

rise e on both sides\[e^{\ln\frac{(T-65)}{125}}=e^{-0.07t} \]