Question

How do I solve this problem? You drive your car on a cold day (20^oF Outside) the engine overheats to about (220^oF). When you park the car the engine begins to cool down. The Temperature T of the engine t minutes after you park satisfies the equation:
ln (T-20/200) = - 0.11t

(a) solve the equation for T

T=

(b) Use part of (a) to find the temperature of the engine after 20 min ( t = 20). Round the answer to 1 decimal place

T=______o F

Answer 1

$ln(T- \frac{20}{200})=-0.11t \\ e^{ln(T- \frac{20}{200})}=e^{-0.11t} \\ T- \frac{20}{200} =e^{-0.11t} \\ T-0.1=e^{-0.11t} \\ T=e^{-0.11t}+0.1$
Then, now that we have solved for T, we can evaluate and solve for t=20 minutes.
$T=e^{-0.11t}+0.1 \\ T=e^{-0.11*20}+0.1 \\ T=e^{-2.2}+0.1 \\ T=0.11+0.1 \\ T=0.21$