CPM Homework Help : PC Problem 4-118

An exponential function passes through the points $(1, 70)$ and $(3, 145)$ . The function has a horizontal asymptote at $y = 10$ . Find an equation for the function.

Step 1:

Write the general equation for this problem.

Step 2:

Substitute the points in for $(x, y)$ , creating two equations and two unknowns.

Step 3:

Subtract $10$ on both sides.
Then divide one equation by the other.

Step 4:

Substitute the $b$ -value back into one of the original equations and solve for $a$ . Then substitute $a$ and $b$ into the general equation.

Answer 1:

$y = a(b^x) + 10$

Answer 2:

$145 = a(b^3) + 10$
$70 = a(b^1) + 10$

Answer 3:

$135 = a(b^3)$
$60 = a(b^1)$
$2.25 = b^2$
$b = 1.5$