Question

How to write an exponential function from a table

Answer 1

Explanation:

I'll show you with an example. I'll make a table and then show you how to find the exponential equation, ok?

x y

0 3

1 12

2 48

3 192

The standard form of an exponential equation is

`y=a(b)^x`

We will take 2 (x,y) coordinates from our table and fit them into the equations to solve for a and b. Using the point (0, 3):

`3=a(b)^0`

b to the 0 power is equal to 1, so the equation then becomes a(1) = 3 so a = 3. We will use the other x, y coordinate along with that a value to now solve for b:

`12=3(b)^1`

b to the first is b, so now that equation becomes 3b = 12 and b = 4. Filling that info back into the standard form:

`y=3(4)^x`

There you go!