CPM Homework Help : INT3 Problem 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.

$\left(1, 15\right)$ and $\left(4, 3885\right), y = –3$
Step 1(a):
Write two equations by substituting the coordinates for $x$ and $y$ .
$15 = ab^{1} − 3$
$3885 = ab^{4} − 3$
Step 2(a):
Use substitution to find the value of $a$ and $b$ . Start by adding $3$ to both sides of the equations.
$a = \frac{18}{b}$
$3888 = \frac{18}{b}b^4$
Step 3(a):
Solve for $b$ . Then solve for $a$ .
Answer (a):
$y = 3\left(6\right)^{x} − 3$

$\left(–2, –7\right)$ and $\left(3, 0.75\right), y = 1$
Hint (b):
Use the same method as part (a).