Find the equation of the exponential function represented by the table below: � x � y 0 0 1 1 1 1 0.5 0.5 2 2 0.25 0.25 3 3 0.125 0.125

Answer 1

Your question formatting got goofed up Vanesa. I'm going to assume the values are as follows:

x | y

---|---

0 | 1

1 | 0.5

2 | 0.25

3 | 0.125

You might be better able to determine the answer if you write the y-values as fractions:

x | y

---|---

0 | 1

1 | 1/2

2 | 1/4

3 | 1/8

You can also think of the fraction denominators as 2 raised to a power:

x | y

---|---

0 | 1

1 | 1/2¹

2 | 1/2²

3 | 1/2³

The basic exponential function can be thought of as y = ab^x

Since each consecutive term increase by a factor of 1/2, can use see that b = 1/2?

And, when x = 0, since b⁰ = 1, then a must equal 1.

So the function is y = (1)(1/2)^x or just y = (1/2)^x