CPM Homework Help : INT3 Problem 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.

Hint:

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

$\left(–1, –0.2\right)$ and $\left(4, 2499\right), y = –1$
Hint (a):
Use the given points and asymptote to write and solve a system of two equations.
Step (a):
$-0.2 = ab^{-1} – 1 \ \ \ \ \ \ \ \ 2499=ab^4-1$

$\left(2, 7.96\right)$ and $\left(4, 7.1536\right), y = 7$
Answer (b):
$y = 6(0.4)^x + 7$