Question

What exponential function is the best fit for the data in the table?

x f(x)

2 -3

3 0

4 12


f(x)=4(4)^(x-1)+4
f(x)=4(4)^(x-1)-4
f(x)=1/4(4)^(x-1)+4
f(x)=1/4(4)^(x-1) -4

Answer 1

f(x)=1/4(4)^(x-1) -4

Explanation:

The negative value for x=2 tells you that the vertical offset cannot be positive. That rules out the 1st and 3rd choices.

You can try x=2 in the remaining functions to see which works:

f(2) = 4(4^(2-1)) -4 = 12 ≠ -3 . . . . . . . . the 2nd choice does not work

f(2) = (1/4)(4^(2-1) -4 = -3 . . . . . . . . . . the 4th choice matches the table