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

12-109.

An exponential function is a function of the form $f\left(x\right) = ab^{x }$.

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

Substitute the points to get two equations.

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

Solve for a and b.

$f\left(x\right) = 4\left(1.5\right)^{x}$

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

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

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

Starting value should be $4$.