T = 24* 0.91^t
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%
[tex]24\times\text{ 91\% = 21.84}[/tex]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:
[tex]\begin{gathered} T_c\text{ = }24\times0.91^t \\ \text{Where T}_{c\text{ }}is\text{ the temperature of the coffee} \\ t\text{ = time} \end{gathered}[/tex]