Question

Which function represent exponential decay?

A. y=1/100(6)*
B. y=(4x)1/2
C. y=2(4/3)*
D. y=12(1/8)*

Answer 1

The function representing exponential decay is D. y = 12(1/8)^x, as the base (1/8) is less than 1, indicating a decay as x increases.

Step-by-step explanation:

The function that represents exponential decay is one in which the base of the exponential expression is between 0 and 1 (excluding 0). Amongst the given options, the only function that fits this criterion is: D. y = 12(1/8)^x. Here, the base is (1/8), which is less than 1 indicating exponential decay.

The decay rate in this context is the amount by which the function decreases over time according to the exponent x. In option D, the decay rate is implied by the base (1/8); each step in x results in the function being multiplied by an additional factor of 1/8, thus decreasing its value.