How to write an exponential function from a table

Step-by-step 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

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):

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:

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

There you go!