Question

(07.06) 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) = one fourth(4)x − 1 + 4
f(x) = one fourth(4)x − 1 − 4

Answer 1

The last choice, f(x)=1/4(4ˣ⁻⁻¹)-4, is correct.

Substituting our values for x, we have:
f(2) = 1/4(4²⁻¹)-4 = 1/4(4¹) - 4 = 1/4(4) - 4= 1 - 4 = -3
f(3) = 1/4(4³⁻¹)-4 = 1/4(4²) - 4 = 1/4(16) - 4 = 4 - 4 = 0
f(4) = 1/4(4⁴⁻¹)-4 = 1/4(4³) - 4 = 1/4(64) - 4 = 16 - 4 = 12

All of the data points fit.