### Home > CCAA8 > Chapter 11 Unit 12 > Lesson CCA: 11.2.2 > Problem11-52

11-52.

The function $f(x)=140(0.7)^x+72$ where $x$ is the time in minutes, could represent the temperature over time of a hot cup of tea placed on the kitchen counter. What does the $72$ represent in the context of this situation? What does the $0.7$ represent?

Separate the function into its component numbers and variables:

$72$: Does this number seem familiar? What is special about $72^{\large \circ }$F?

$x$: What purpose does this number serve in the function? What does the $x$-axis represent?

$0.7$: This number gets smaller as x gets bigger. Could it represent a percentage?

$200$: Could this be the temperature of something? What would this be the temperature of?

$72$ represents room temperature.
The cup of hot tea gets continually closer to $72^{\large \circ }$ as time progresses.

$x$ represents time, probably in minutes, that has passed.

$0.7$ represents the $70\%$ of heat difference that remains after each minute,
as $30\%$ of the difference is lost.

$200$ represents the initial temperature of the tea.