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=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.

50 minutes

Step-by-step explanation:

Given:

Temperature, T = 230°F

Overheat temp, To = 280°F

Ts = 80°F

Cooling rate, r = 0.0058

Since the car can be driven again at 230°F, and when it is 80°F outside, the cooling rate of the car is 0.0058, using Newton's law of cooling, we have:

Substituting figures, we have:

Solving further, let's subtract 80 from both sides, we now have:

Divide both sides by 200:

Let's take the natural log of both sides, we have:

Using logarithm power rule, we have:

= - 0.2877 = - 0.0058t

To find t, let's now divide both sides by -0.0058

50 = t

Therefore, you have to wait for 50 minutes before you can continue driving.