# How do you use the model y=a * b^x to find the model for the graph when given the two points, (4,256) (3,64)?

Aug 14, 2016

$y = {4}^{x}$.

#### Explanation:

Let us denote, by $C ,$ the curve $: y = a \cdot {b}^{x}$.

We observe that the eqn. of $C$ has two unknown consts,, namely,

$a \mathmr{and} b$; and as such, to determine them we need two conds.,

given by pts. on $C$.

Given that, pt. $\left(4 , 256\right) \in C \Rightarrow 256 = a \cdot {b}^{4.} \ldots \ldots \ldots . . \left(1\right)$, and,

$\left(3 , 64\right) \in C \Rightarrow 64 = a \cdot {b}^{3.} \ldots \ldots \ldots \ldots \ldots . \left(2\right)$

To Solve $\left(1\right) \mathmr{and} \left(2\right)$, we divide $\left(1\right)$ by $\left(2\right)$, & get, $b = 4$.

Then, by $\left(2\right)$, we have, $a = 1$.

Therefore, $C$ is given by, $y = {4}^{x}$.