Question

Write an exponential function for the set of points.
x 0 1 2 3 4
f(x) 27 9 3 1 13
A. f(x)=(13)x
B. f(x)=3x
C. f(x)=27(13)x
D. f(x)=27(3)x
Does this represent exponential growth or decay?
A. growth
B. decay

Answer 1

f(x) = 27*(1/3)^x, which is choice C.

Reason: f(0)=27 so a=27, and the common ratio is f(1)/f(0)=9/27=1/3, so f(x)=27(1/3)^x. Since the base 1/3 < 1, this is exponential decay (choice B).

(Note: the table entry f(4)=13 appears to be a typo — with this function f(4)=27*(1/3)^4 = 1/3.)