### Home > GB8I > Chapter 8 Unit 9 > Lesson INT1: 8.2.3 > Problem8-121

8-121.

An exponential function of the form $f(x) = ab^x$ that passes through the points $(2,2)$ and $(4, \frac { 1 } { 2 })$.

1. What is the equation 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 $(4,\frac{1}{2})$.
Equation $1$: $2 = ab^2$
Equation $2$: $\frac{1}{2} = ab^4$

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 $a$.

2. Use the equation to sketch a graph of the function.

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.