# How do you find an exponential function of the form y=ab^x whose graph passes through the points (2,1) and (3,2)?

May 13, 2016

$a = \frac{1}{4} \mathmr{and} b = 2$. And so, $y = {2}^{x} / 4$..

#### Explanation:

On a semi-log (x vs Y=log y) the graph of $y = a {b}^{x}$ will be a

straight line for Y = log y = log a + x log b#.

Substituting (x, y) = (2, 1) and (3.2), we get

$0 = \log a + 2 \log b \mathmr{and} \log 2 = \log a + 3 \log b$.

So, $a = \frac{1}{4} \mathmr{and} b = 2$.