### Home > INT1 > Chapter Ch11 > Lesson 11.2.1 > Problem11-49

11-49.

Write the equation of an exponential function that passes through each pair of points.

1. $(1, 7.5) \text{ and } (3, 16.875)$

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 2nd 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. $(−1, 1.25) \text{ and } (3, 0.032)$

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