You are taking a road trip in a car without A/C. The temperature in the car is 90 degrees F. You buy a cold pop at a gas station. Its initial temperature is 45 degrees F. The pop's temperature reaches 60 degrees F after 21 minutes.

Given that
T = (T_0-A)e^(-kt)+A
where T = the temperature of the pop at time t.
T_0 = the initial temperature of the pop.
A = the temperature in the car.
k = a constant that corresponds to the warming rate.
and t = the length of time that the pop has been warming up.

How long will it take the pop to reach a temperature of 81.25 degrees F?

Question

You are taking a road trip in a car without A/C. The temperature in the car is 90 degrees F. You buy a cold pop at a gas station. Its initial temperature is 45 degrees F. The pop's temperature reaches 60 degrees F after 21 minutes.

 Given that 
T = (T_0-A)e^(-kt)+A 
 where T =  the temperature of the pop at time t.
T_0 =  the initial temperature of the pop. 
A =  the temperature in the car. 
k =  a constant that corresponds to the warming rate.
 and t =  the length of time that the pop has been warming up.


 How long will it take the pop to reach a temperature of 81.25 degrees F?