Skip to section navigation Skip to main content

A Deeper Look at Exponential Functions

Examine the graph of the exponential model with the scatter plot:

This graph is a scatter plot displaying the temperatures of a cup of coffee as it cools over the period of thirty minutes.  The graph is titled ‘Coffee Temperatures.’  The horizontal axis is labeled ‘Time (in minutes)’ and extends from negative 5 to 32.  The vertical axis is labeled ‘Temperature (in degrees Fahrenheit)’ and extends from negative 20 to 240.  The graph displays the following ordered pairs:  (0, 195), (5, 160), (10, 134), (15, 115), (20, 101), (25, 90), and (30, 82).  The curve defined by function g of x = 187.374 times 0.971 to the power of x is drawn through the scatter plot.

Even though the data should follow an exponential model, the prediction for 60 minutes does not make sense.  The temperature indicates that the coffee should be frozen but without any additional cooling agents, the coffee should only cool to room temperature after an hour.

If an exponential curve is the best fit for the data, why is this equation not the best fit?


< Previous Next >