Question

The temperature of a cup of coffee t minutes after it has been poured is described by the function C(t) = 20 + 60(0.95)^t . a. How many minutes does it take for the coffee to cool to a temperature of d degrees? b. About how fast is the temperature dropping when t = 1?

Answer 1

The temperature of coffee 10 minutes after it was poured (120 F) will help in solving the constant “a”. 
120 = 120(2 ^ 10a) + 60 
2 ^ -1 = 2 ^ 10a 
a = -1/10 
The temperature of coffee 30 minutes after it was poured is: 
F = 120 ( 2 ^ -30/10) + 60 
F = 120 * 1/ 8 + 60 
F = 15 + 60 
F = 75