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.

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497