Home > CCA > Chapter 7 > Lesson 7.2.2 > Problem7-96

7-96.

Find an exponential function that passes through each pair of points.

1. $\left(1, 7.5\right)$ and $\left(3, 16.875\right)$

To start, write a system of equations in the form $y =ab^{x}$ by substituting the points in for $x$ and $y$.

$16.875 = ab^{3}$

$7.5 = ab^{1}$

Divide the $2$nd equation into the first to eliminate $a$.

$2.25 = b^{2}$

Solve for $b$.

Substitute the $b$ value you found into one of the original equations.
Solve for $a$.
Substitute both $a$ and $b$ back into the original equation with along with $x$ and $y$.

$y = 5\left(1.5\right)^{x}$

1. $\left(−1, 1.25\right)$ and $\left(3, 0.032\right)$

$y = 0.5\left(0.4\right)^{x}$