Question

A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries three-fourths, three-halves, 3, 6, 12.
Which exponential function is represented by the values in the table?

f(x) = 3(2x)
f(x) = 2(2x)
f(x) = 3(3x)
f(x) = 2(3x)

Answer 1

f(x) = 3·2^x.

Reason: f(0)=3 gives the factor 3, and successive ratios f(1)/f(0)=6/3=2 so the base is 2, hence f(x)=3·2^x (matches f(−2)=3/4, f(−1)=3/2, f(1)=6, f(2)=12).