### Home > CCA > Chapter 7 > Lesson 7.2.3 > Problem7-106

7-106.

Find the equation of an exponential function that passes through the points $\left(2, 48\right)$ and $\left(5, 750\right)$.

Substitute the values for $x$ and $y$.

$y = ab^{x}$

$750 = ab^{5}$

$48=ab^2$

Solve both equation for $a$.

$a=\frac{48}{b^{2}}$

$a=\frac{750}{b^{5}}$

Set the equations equal to each other. Solve for b by multiplying both sides of the equation by $b^{5}$.

Substitute $b$ into one of the equations from Step 1 and solve for $a$. After you know $a$ and $b$, write the equation.

$y = 7.68\left(2.5\right)^{x}$