### Home > CCA2 > Chapter 2 > Lesson 2.1.5 > Problem2-72

2-72.

Find the equation of an exponential function that passes through each pair of points.

1. $(2,9)$ and $(4,324)$

Use the equation $y=ab^x$ to help you here. Begin by substituting one of the points for $x$ and $y$.

Next, substitute the other ordered pair for $x$ and $y$.

$9=ab^{2}$

$a=\frac{9}{b^{2}}$

Use substitution, and solve for $b$.

$324=ab^{4}$

$a=\frac{324}{b^{4}}$

Now, solve for $a$.

$\frac{9}{b^{2}}=\frac{324}{b^{4}}$

$9b^{4}=324b^{2}$

$9b^{2}=324$

$b^{2}=36$

$b=6$

$y = 0.25\cdot 6^{x}$

1. $(−1,40)$ and $(0,12)$

Look at the hints in part (a).

$y=12\cdot0.3^x$

Use the eTool below to help you solve part (a).
Click the link at right for the full version of the eTool: CCA2 2-72a HW eTool

Use the eTool below to help you solve part (b).
Click the link at right for the full version of the eTool: CCA2 2-72b HW eTool