You are taking a road trip in a car without A/C. The temperture in the car is 86 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 47 minutes. Given that \frac{T-A}{T_0 - A} = e^{-kt} 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 82.25 degrees F?

Question

You are taking a road trip in a car without A/C. The temperture in the car is 86 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 47 minutes. Given that \frac{T-A}{T_0 - A} = e^{-kt} 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 82.25 degrees F?