The data in the table shows the temperature for a cup of coffee after it is poured into the cup. The initial temperature of the coffee is F. Which one of the following functions is the best model for this data?
C) None of these options

Question

The data in the table shows the temperature for a cup of coffee after it is poured into the cup. The initial temperature of the coffee is F. Which one of the following functions is the best model for this data? 
C) None of these options

Quizplus · Accepted Answer

The temperature of the coffee decreases exponentially with time as it cools down. The function that models this behavior is an exponential decay function of the form f(t) = ae^(-kt) where f(t) is the temperature of the coffee at time t, a is the initial temperature of the coffee, and k is the rate of cooling. 
By examining the given data, it can be seen that the temperature decreases exponentially with time. The best-fitting function for this data is e^(0.16t), so the answer is D.

The Data in the Table Shows the Temperature for a Cup