Question

I need to be able to take a set of data, and find it's exponential function.​

Answer 1

The process below should work.

Explanation:

Let's pretend we have these two points we are trying to find an exponential equation for: (-2,6) and (2,1).

Exponential equations are of the form
`y=a \cdot b^x` where we must find
`a` and
`b`.

So you enter both points into that equation giving you:

`6=a \cdot b^(-2)`

`1=a \cdot b^(2)`

I'm going to divide equation 1 by 2 because if I do the a's will cancel and I could solve or b.

`(6)/(1)=(a \cdot b^(-2))/(a \cdot b^2)`

`6=(b^(-2))/(b^2)`

By law of exponent, I can rewrite the right hand side:

`6=b^(-2-2)`

`6=b^(-4)`

Now do ^(-1/4) on both sides to solve for b:

`6^(-1)/(4)=b`

Now we use one of the equations along with our value for b to find a:

`1=a \cdot b^2` with
`b=6^{(-1)/(4)}`

`1=a \cdot (6^{(-1)/(4)})^2`

Simplify using law of exponents:

`1=a \cdot 6^{-(1)/(2)}`

Multiply both sides by 6^(1/2) to solve for a:

`6^{(1)/(2)}=a`

`y=a \cdot b^x` with
`a=6^{(1)/(2)} \text{ and } b=6^{(-1)/(4)}` is:

`y=6^(1)/(2) \cdot (6^{(-1)/(4))^x`

We can simplify a smidgen:

`y=6^(1)/(2) \cdot (6)^(-x)/(4)`