# How do you find the exponential function formula for the points g(2)=45 and g(4)=405?

May 10, 2016

An exponential function is generally of the form $y = a {c}^{x}$

#### Explanation:

$y = a {c}^{x}$

Writing a system of equations to solve for $a \mathmr{and} c$

$45 = a {c}^{2}$

$405 = a {c}^{4}$

$\frac{405}{c} ^ 4 = a$

$45 = \frac{405}{c} ^ 4 \left({c}^{2}\right)$

$45 = \frac{405}{c} ^ 2$

$45 {c}^{2} = 405$

${c}^{2} = 9$

$c = 3$

$45 = a \left({3}^{2}\right)$

$45 = 9 a$

5 = a#

Therefore, your equation is $y = 5 \times {3}^{x}$