Exponential Regression Model Example
(when doing an exponential regression, the y-values must be greater than 0)

Data:  The data at the right shows the cooling temperatures of a freshly brewed cup of coffee after it is poured from the brewing pot into a serving cup.  The brewing pot temperature is approximately 180º F.

Time (mins)
Temp ( º F)
0
179.5
5
168.7
8
158.1
11
149.2
15
141.7
18
134.6
22
125.4
25
123.5
30
116.3
34
113.2
38
109.1
42
105.7
45
102.2
50
100.5
 Task: a.) Determine an exponential regression model equation to represent this data. b.) Graph the new equation. c.) Decide whether the new equation is a "good fit" to represent this data. d.) Based upon the new equation, what was the initial temperature of the coffee? e.) Interpolate data:  When is the coffee at a temperature of 106 degrees? f.) Extrapolate data:  What is the predicted temperature of the coffee after 1 hour? g.) In 1992, a woman sued McDonald's for serving coffee at a temperature of 180º that caused her to be severely burned when the coffee spilled.  An expert witness at the trial testified that liquids at 180º will cause a full thickness burn to human skin in two to seven seconds.  It was stated that had the coffee been served at 155º, the liquid would have cooled and avoided the serious burns.  The  woman was awarded over 2.7 million dollars.  As a result of this famous case, many restaurants now serve coffee at a temperature around 155º.   How long should restaurants wait (after pouring the coffee from the pot) before serving coffee, to ensure that the coffee is not hotter than 155º ? h.) If the temperature in the room is 76° F, what will happen to the temperature of the coffee, after being poured from the pot, over an extended period of time?