Question

Toby writes an exponential function f(x) that meets the following two conditions:
I. The value of f(1) is 6.
II. The value of f(x) doubles for each increase of 1 in the x values.
Which equation could represent the exponential function that Toby wrote?
A f(x) = 3(2)*
B f(x) = 2(6)*
c f(x) = 6(2)*
D f(x) = 2(3)*

Answer 1

II.  f(x) doubles for each increase of 1 in the x values.  Thus, r must be 2, and so we our ar^1 = 6 from ( I ) above becomes  f(x) = a*2^x.  Applying the restriction ar^1 = 6 results in f(1) = a*2^1 = 6, or a = 3.

Then f(x) = ar^x becomes f(x) = 3*2^2 (Answer A)