A function commonly used to represent bounded growth of a real-world function value is the exponential-linear combination function of the general form , in which represents the horizontal asymptote toward which the values of converge. Use the following graph to determine and using the point , then write an exponential-linear combination function that models the graph.
Note: If the -axis is missing, press the ZoomFit button in the upper right corner of the applet.

Use the graph to identify the asymptote toward which the function values converge as the values of increase.

Determine the value of in the general form of the combination function.

Update the general form of the combination function with the value of .

Find algebraically and compare it to the graph.

Use the point to find the value of .

Write the exponential-linear combination function.

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