Example 1
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.