Question

Write an exponential function for the set of points

x | 0 | 1 | 2 | 3 | 4
f(x) | 27 | 9 | 3 | 1 | 1/3

Answer 1

The function is
`f(x) = 27((1)/(3))^x`

Explanation:

Compare the y values. Notice that the y values are all multiples of 3 and they decrease by dividing by 3 each time. This suggests the base is 1/3.

Now check when x = 0. This is the initial value since the zero exponent gives an output of 1. So the only way for (0,27) to be a point is for 27 to e multiplied as the initial value. The function is
`f(x) = 27((1)/(3))^x`