Question

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

Answer 1

Answer:

The process below should work.

Step-by-step 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.

$\frac{6}{1}=\frac{a \cdot b^{-2}}{a \cdot b^2}$

$6=\frac{b^{-2}}{b^2}$

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:

$6^\frac{-1}{4}=b$

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

$1=a \cdot b^2$ with $b=6^{\frac{-1}{4}}$

$1=a \cdot (6^{\frac{-1}{4}})^2$

Simplify using law of exponents:

$1=a \cdot 6^{-\frac{1}{2}}$

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

$6^{\frac{1}{2}}=a$

$y=a \cdot b^x$ with $a=6^{\frac{1}{2}} \text{ and } b=6^{\frac{-1}{4}}$ is:

$y=6^\frac{1}{2} \cdot (6^{\frac{-1}{4})^x$

We can simplify a smidgen:

$y=6^\frac{1}{2} \cdot (6)^\frac{-x}{4}$