Suppose youre driving your car on a cold winter day 10F outs

Suppose you\'re driving your car on a cold winter day (10°F outside) and the engine overheats (at about 210°F). When you park, the engine begins to cool down. The temperature T of the engine t minutes after you park satisfies the equation

Ln(T-10/200)=-0.13t

Solve the equation forT.

Use part (a) to find the temperature of the engine after 40 min (t = 40). (Round your answer to one decimal place.) T=F

After how many seconds is the current 3 A? (Round your answer to three decimal places.)

Solution

ln(T -10/200)=-.13t

writing it in exponential form

T-10/200= e^-.13t

T-10= 200(e^-.13t)

T= 200(e^-.13t) +10

and at t=40

T=200(e^-.13×40) +10

T= 11.1 ^° F