### Home > PC3 > Chapter 8 > Lesson 8.1.2 > Problem8-30

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.

Write the general equation for this problem.

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

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

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

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

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

Divide the equations and solve for $b$.

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

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