Question

You are driving on a hot day when your car overheats and stops running. The car overheats at 280°F and can be driven again at 230°F. When it is 80°F outside, the cooling rate of the car is r is equal to 0 point 0 0 5 8 $r=0.0058$ r=0.0058​ . How long do you have to wait until you can continue driving? Use Newton's Law of Cooling to solve the problem. Round your answer to the nearest whole minute.

Answer 1

Answer: 50 minutes

Explanation:

Given the following :

Overheating temperature T0 = 280°F

Driving temperature T = 230°F

Ourltside temperature TR = 80

Cooling rate r = 0.0058

Using Newtons law of cooling

T = (T0 - TR)e^(-0.0058t) + 80

230 = 200e^(-0.0058t) + 80

150 = 200e^(-0.0058t)

(150/200) = e^(-0.0058t)

0.75 = e^(-0.0058t)

In 0.75 = (-0.0058t)

-0.2877 = -0.0058t

t = - 0.2877/0.0058

t = 49.60

t = 50 minutes (to the nearest whole number)