An exponential decay function takes the form y = a * b^x, where a > 0 and 0 < b < 1. Therefore, to figure out which of the given options is an exponential decay function, we need to inspect the coefficients and verify if they satisfy these conditions.
Let's examine option A. In this function, a = 3/4 and b = 7/4.
The 'a' value satisfies the condition as 'a' must be greater than 0 and 3/4 is greater than 0.
However, for the 'b' value, we apply the condition that 'b' must be between 0 and 1(exclusive), and we notice that 7/4 isn't less than 1. Therefore, the function f(x) = 3/4 * (7/4)^x does not satisfy the conditions required for an exponential decay function.
Next, let's examine option B. In this function, a = 2/3 and b = 4/5.
The 'a' value is 2/3, which is greater than 0, thus satisfying the 'a' condition.
The 'b' value is 4/5, which is between 0 and 1(exclusive), satisfying the 'b' condition.
Therefore, the function f(x) = 2/3 * (4/5)^(-x) satisfies the conditions required for an exponential decay function.
So, the function in option B: f(x) = 2/3 * (4/5)^(-x) is an exponential decay function.