Question

A cup of hot coffee will, over time, cool down to room temperature. The principle of physics governing the process is Newton's Law of Cooling. The temperature (in degrees Fahrenheit) of a cup of coffee can be modelled by the following equation:

f(t)=80+120e^-0.08t

Explain, using the structure of the expression 80+120e^-0.08t, why the coffee temperature decreases as time elapses (8 points).

Answer 1

Explanation:

f(t) = 80 + 120 e^(-0.08 t)

The exponent is negative, so this is an example of exponential decay. As t increases, the exponent becomes more and more negative. So e^(-0.08 t) gets closer and closer to 0. Meaning f(t) gets closer and closer to 80.