Members of a Florida high school’s nature club tracked the estimated number of tree frogs living in a nearby cypress tree for 9 weeks. The estimates are based on the recorded volume of the frogs’ singing over a 24-hour period on the same day of each week. The table shows the club’s estimates for the number of frogs per week, with the independent variable representing time in weeks.
Use a graphing calculator to graph the data. Then, use the graph to find both an exponential function of the form and a power function of the form to fit the data. Compare how closely each function equation models the data on the graph.

Create a scatter plot of the table values using a graphing calculator.

Next, use the graphing calculator to fit the data to an exponential function and a power function.

Write the equations of the calculated exponential and power functions from using the variables and .

Plot the exponential and power functions from the previous step on the scatter plots produced by the tree-frog data.

Describe how well the exponential function fits the data points.

Describe how well the power function fits the data points.

Determine which function type, exponential or power, best fits the data.

This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit www.walch.com for more information.