The function y = 12((1)/(8))ˣ represents exponential decay because the base (1/8) is between 0 and 1, fitting the criteria of an exponential decay function where the values decrease as the exponent increases.
The function that represents exponential decay must have a base between 0 and 1. In the given options, the function y = 12((1)/(8))ˣ is the correct one because (1/8) is between 0 and 1 and for every increase in x, the value of y will decrease. Exponential decay occurs when the decay rate is positive, and the base of the exponential function is less than one which results in the function's values decreasing as x increases.
The decay rate for this function can be inferred from the exponent base (1/8), indicating that as x increases, the value of y will decrease by an eighth in each step. This is a typical feature of an exponential decay function where the rate of change decreases over time.