Step 1 :The problem is asking for a function that represents the population of bats after t years, given that the population is growing exponentially at 6% per year. We also need to find the monthly rate of change.
Step 2 :To solve this, we can use the formula for exponential growth, which is \(P(t) = P0 * e^{rt}\), where \(P0\) is the initial population, \(r\) is the rate of growth, and \(t\) is time.
Step 3 :In this case, \(P0\) is 6600, \(r\) is 6% or 0.06, and \(t\) is the number of years.
Step 4 :To find the monthly rate of change, we can divide the annual rate of change by 12.
Step 5 :The function to represent the population of bats after t years is \(f(t) = 6600 * e^{0.06t}\). The monthly rate of change is 0.5%.
Step 6 :Final Answer: The function is \(f(t) = 6600 * e^{0.06t}\) and the monthly rate of change is \(\boxed{0.5\%}\).