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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.

Write the general equation for this problem.

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

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

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

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

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

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