Answer: The function that represents exponential decay is:
D. f(x) = 268(0.86)^x
This function has a base of 0.86, which is less than 1. As x increases, the value of the function decreases exponentially. This is the characteristic of exponential decay, where the value of a quantity decreases at a constant percentage rate over time.
Option A, f(x) = 0.25(1.06), represents exponential growth, as the base (1.06) is greater than 1.
Option B, f(x) = 18 + 0.9x, represents linear growth, as the value of the function increases linearly with x.
Option C, f(x) = 412 + 1.03x, also represents linear growth, as the value of the function increases linearly with x.
Explanation: