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

Question

x. y

0. 0.2

1. 0.6

2. 1.8

3. 5.4

Answer 1

The generic form of an exponential is y = a•b^x where a and b must be determined by the situation (data points in this case).

First, plug in the point (x, y) of (0, 0.2):

0.2 = a•b⁰

since anything (except 0) raised to the zero power is 1, b⁰ = 1 and:

0.2 = a

Now our equation is y = 0.2•b^x so lets plug in another data point. How about (1, 0.6)? So:

0.6 = 0.2•b¹

0.6/0.2 = b

b = 3

So now, our equation is:

y = 0.2•3^x

Let's make sure it works for the other data points:

1.8 = 0.2•3²

1.8/0.2 = 3²

9 = 9 check

5.4 = 0.2•3³

5.4/.2 = 3³

27 = 27 check

So the equation checks out

y = 0.2•3^x