### Home > GB8I > Chapter 9 Unit 10 > Lesson INT1: 9.1.1 > Problem9-10

9-10.

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

Create a system of equations using the general form of the exponential function: $y = a·b^x$

Substitute $x$ and $y$ into the equation $y = a·b^x$

$48=ab^2 \quad \quad 750=ab^5$

Solve both equations and use the equal values method to make one equation. Solve for $b$.
Then substitute $b$ into one equation and solve for $a$.

$\frac{48}{b^2}=a \quad \quad \frac{750}{b^5}=a$

$\frac{48}{b^2}=\frac{750}{b^5}$

$y = 7.68(2.5)^x$