Function f(x) = 500(0.97)^x represents a 3% decrease per month and the correct option is C.
Let's analyze the answer choices:
A. f(x) = 500(1.03)^x: This function represents an exponential growth with a base of 1.03. Since the population is decreasing, this function cannot be the correct answer.
B. f(x) = 500(0.03)^x: This function represents an exponential decay with a base of 0.03. The base is too small to represent a 3% decrease.
C. f(x) = 500(0.97)^x: This function represents an exponential decay with a base of 0.97. This base represents a 3% decrease, so this function could be the correct answer.
D. f(x) = 500(1.3)^x: This function represents an exponential growth with a base of 1.3. Since the population is decreasing, this function cannot be the correct answer.
We can check our answer by calculating the population after one month using each function. The initial population is 500 and the population decreases by 3% each month.
Function A: 500 * (1.03)^1 ≈ 515
Function B: 500 * (0.03)^1 ≈ 15
Function C: 500 * (0.97)^1 ≈ 485
Function D: 500 * (1.3)^1 ≈ 650
Only function C results in a population of 485 after one month, which is consistent with the given information.
Therefore, the correct answer is C. f(x) = 500(0.97)^x.