### Home > INT3 > Chapter 7 > Lesson 7.2.5 > Problem7-118

7-118.

Write the equation of an exponential function of the form $y = ab^{x} + k$ that passes through each of the following pairs of points and has the given asymptote.

1. $\left(1, 15\right)$ and $\left(4, 3885\right), y = –3$

Write two equations by substituting the coordinates for $x$ and $y$.

$15 = ab^{1} − 3$
$3885 = ab^{4} − 3$

Use substitution to find the value of $a$ and $b$. Start by adding $3$ to both sides of the equations.

$a = \frac{18}{b}$

$3888 = \frac{18}{b}b^4$

Solve for $b$. Then solve for $a$.

$y = 3\left(6\right)^{x} − 3$

1. $\left(–2, –7\right)$ and $\left(3, 0.75\right), y = 1$

Use the same method as part (a).