Question

A cup of coffee is initially at a temperature of 96°F. The difference between its temperature and theroom temperature of 72°F decreases by 9% each minute write a function describing the temperature of the coffee as a function of time

Answer 1

T = 24* 0.91^t

Step-by-step explanation:

The initial temperature of coffee = 96°F

The temperature at room temperature = 72°F

The difference in temperature between initial temperature and room temperature:

96°F - 72°F = 24°F

We are told the difference decrease every minute by 9%

In one minute, decrease:

100% - 9% = 91%

`24*\text{ 91\% = 21.84}`

Due to decrease every minute, it would be an exponential function. The decrease raised to power of time.

The function describing the temperature of the coffee as a function of time:

`\begin{gathered} T_c\text{ = }24*0.91^t \\ \text{Where T}_{c\text{ }}is\text{ the temperature of the coffee} \\ t\text{ = time} \end{gathered}`