Question

Which is an exponential growth function?

f(x) = 6(0.25)x
f(x) = 0.25(5.25)x
f(x) = –4.25x
f(x) = (–1.25)x

Answer 1

Exponential growth requires the base b in f(x) = a·b^x to be greater than 1.

- 6(0.25)^x: base 0.25 < 1 → exponential decay.
- 0.25(5.25)^x: base 5.25 > 1 → exponential growth.
- −4.25^x (interpreted as −(4.25)^x): values are negative (magnitude grows) but not a positive exponential growth function.
- (−1.25)^x: negative base (not a standard exponential growth for all real x).

So the exponential growth function is f(x) = 0.25(5.25)^x.