# How do you write exponential function for a graph that includes given points (4,8) (6,32)?

Dec 3, 2016

Please see the explanation.

#### Explanation:

$y \left(4\right) = 8 = a \left({b}^{4}\right)$
$y \left(6\right) = 32 = a \left({b}^{6}\right)$

$\frac{32}{8} = a \frac{{b}^{6}}{a} \left({b}^{4}\right)$

$4 = {b}^{2}$

$b = 2$

$y \left(4\right) = 8 = a \left({2}^{4}\right)$

$8 = a \left({2}^{4}\right)$

$a = \frac{1}{2}$

$y = \frac{1}{2} \left({2}^{x}\right)$

$y = \left({2}^{-} 1\right) \left({2}^{x}\right)$

$y = {2}^{x - 1}$