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)?

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Answer 1 · 2016-08-14T06:37:00

$y=4^x$ .

Let us denote, by $C,$ the curve $: y=a*b^x$ .

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

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

given by pts. on $C$ .

Given that, pt. $(4,256) in C rArr 256=a*b^4............(1)$ , and,

$(3,64) in C rArr 64=a*b^3.................(2)$

To Solve $(1) and (2)$ , we divide $(1)$ by $(2)$ , & get, $b=4$ .

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

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

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