CPM Homework Help : PC3 Problem 8-30

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

Step 1:

Write the general equation for this problem.

Answer 1:

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

Step 2:

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

Answer 2:

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

Step 3:

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

Answer 3:

$135=ab^3$
$60=ab^1$

Step 4:

Divide the equations and solve for $b$ .

Answer 4:

$2.25=b^2$
$b=1.5$

Step 5:

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