The exponent needs to reflect the number of years (15), not a random value (5, 4, 3, or 2). Therefore, the correct answer is 5^15. Hence the correct option is d.
In an exponential expression representing population growth, the exponent typically represents the number of growth periods (e.g., years, generations). In this case, we're dealing with a 15-year period.
Let's analyze the options:
A) 2⁵: 5 represents the base (initial rabbit population), but 5 doesn't reflect the time period (15 years).
B) 3⁴: Similar to A, 4 doesn't represent the 15-year period.
C) 4³: Again, 3 doesn't correspond to the 15-year timeframe.
D) 5^15: Here, 5 represents the initial population and 15 accurately reflects the number of years (growth periods). This makes 5^15 the correct expression for the rabbit population's growth over the entire 15 years. Hence the correct option is d.