Question

Find the equation of the exponential function represented by the table below:

x y
0 0.2
1 0.8
2 3.2
3 12.8

Answer 1

Explanation:

If this is an exponential function, it is of the form

`y=a(b)^x` where x and y are coordinates from your table, a is the intial value, and b is the growth/decay rate. To find out what the equation is that represents this data, choose 2 points and solve first for a and then for b. Just a hint: If at all possible, choose the coordinate that gives you an x of 0. You'll see why in a minute.

I chose the first 2 points from your table: (0, .2) and (1, .8). Solving first for a:

`.2=a(b)^0` The reason to choose the x of 0 as one of your points is because anything raised to the power of 0 is 1. So our equation then becomes:

`.2=a(1)` so

a = .2 Easy enough.

Now use that value along with the other coordinate to solve for b:

`.8=.2(b)^1` b to the first is just b, so,

.8 = .2b

Divide both sides by .2 and you'll get that

b = 4

The equation, then, is

`y=.2(4)^x` which is growth, since the value for b is greater than 1.