Michael is driving a car in a cold winter day with a temperature of 20 degree F and the engine of the car will overheat at about 220 degree F and if the car is parked the engine will cool down. Suppose that the equation ln(T−20200)=−0.11t where T is the temperature of the engine and t is the minutes after you park.
a.) Solve the equation for T.
b.) Determine the temperature of the engine after 20 min (t = 20) by using your answer in part(a).
a.)
ln(T−20200)=−0.11teln(T−20200)=e−0.11tT−20200=e−0.11tT−20=200e−0.11tT=20+200e−0.11t
b.) if t=20 mins, then
T=20+200e−0.11(20)T=42.16∘F
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