### Home > INT2 > Chapter 12 > Lesson 12.2.3 > Problem12-109

12-109.

An exponential function is a function of the form $f(x) = ab^x$ .

1. What is the equation of an exponential function that passes through the points $(1, 6)$ and $(5, 30.375)$?

Substitute the points to get two equations.

$6 = ab^1$
$30.375 = ab^5$

Solve for $a$ and $b$.

$f(x) = 4(1.5)^x$

2. What does the $b$value from part (a) tell you about the function?

$\text{How are the graphs of }f(x) = 2^x, f(x) = 3^x, f(x) = \left(\frac{1}{2}\right)^x \text{ different?}$
Starting value should be $4$.

3. Write a situation that could be modeled by this equation.