### Home > INT1 > Chapter Ch8 > Lesson 8.2.3 > Problem 8-121

8-121.

An exponential function of the form

*f*(*x*) =*ab*that passes through the points (2, 2) and (4,^{x}). *8-121 HW eTool*(Desmos). Homework Help ✎What is the equation of the function?

Use the equation to sketch a graph of the function.

Read Math Notes box in Lesson 8.2.2 on curve fitting an exponential function.

Create two equations using the points (2,2) and (4,1/2).

Equation 1: 2 = *ab*²

Equation 2: 1/2 = *ab*^{4}

Isolate *a* for both equations. Use the Equal Values Method to solve for *b*.

Substitute *b* into one of the original equations, and solve for *a*.

Use the eTool below to help solve the problem.

Click the link at the right to view full version of the eTool: Int1 8-121 HW eTool.