# How do you find formulas for the exponential functions satisfying the given conditions h(0)=3 and h(1)= 15?

Oct 25, 2016

An exponential function is a function of the form $y = a {b}^{x}$.

Knowing the inputs and outputs of the function, we can write a systems of equations, with respect to $a$ and $b$ to represent the problem.

$3 = a {b}^{0}$
$15 = a {b}^{1}$

The simplest way of solving this system will be using the fact that ${n}^{0} , n \in \mathbb{R} = 1$. So, we immediately know that $a = 3$.

We insert $a = 3$ into the second equation to get $b = 5$.

So, the exponential function is $y = 3 {\left(5\right)}^{x}$.

Hopefully this helps!