CPM Homework Help : PC Problem 8-109

An exponential function has an asymptote at $y = 10$ . The function passes through the points $\left(4, 6\right)$ and $\left(7, 8\right)$ . Find the $y$ -intercept for the function exactly and then calculate it to three decimal places.

Step 1:

Write the exponential form:

$y = \left(a\right)b^{x} + 10$

Step 2:

Substitute each point in for $\left(x, y\right)$ forming two equations and two unknowns.

$6 = \left(a\right)\left(b\right)^{4} + 10$
$8 = \left(a\right)\left(b\right)^{7} + 10$

Step 3:

Solve for ' $a$ ' and ' $b$ ' and substitute the contants into the function.

Step 4:

Using the new function, substitute ' $0$ ' for ' $x$ ' and simplify. This is the $y$ -intercept.