### Home > INT3 > Chapter 7 > Lesson 7.2.2 > Problem7-71

7-71.

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.

In this case, the horizontal asymptote is the vertical shift, or the $k$ in the equation.

1. $\left(–1, –0.2\right)$ and $\left(4, 2499\right), y = –1$

Use the given points and asymptote to write and solve a system of two equations.

$-0.2 = ab^{-1} – 1 \ \ \ \ \ \ \ \ 2499=ab^4-1$

1. $\left(2, 7.96\right)$ and $\left(4, 7.1536\right), y = 7$

$y = 6(0.4)^x + 7$