Sure, we can model the attendance over the years using an exponential decay function since the percentage decrease is constant every year. Let's denote the year as 'x'. This is relative to the year 2000. Hence, for the year 2000, x is 0; for 2001, x is 1; for 2002, x is 2, and so on.
The general form of an exponential decay function is:
A = A0 * (1 - r) ^ x
where:
- A is the final amount
- A0 is the initial amount (i.e., the attendance in 2000 which is 18,000)
- r is the rate of decrease (i.e., the yearly attendance decrease which is 5.5% or 0.055 when represented as a decimal)
- x is the number of time periods that have passed (i.e., the number of years since 2000)
So in our case, the function governing the attendance since the year 2000 is:
A = 18000 * (1 - 0.055) ^ x
This function allows us to calculate the attendance for any year since 2000 by substituting the appropriate value for 'x' (i.e., the number of years since 2000). For example, to calculate the attendance in 2003 (3 years after 2000), we would replace 'x' with 3 in our function.
Please don't forget that interest rates are usually compounding, so in our case, the 5.5% annual decrease is re-applied to the remaining attendance balance at the end of each year. Hence, the reason for using an exponential function.