Final answer:
The town's population is increasing at a yearly rate of 2%, determined by the base of the exponential function in P(n) = 2000(1.02)ⁿ.
Step-by-step explanation:
The population growth of a small town since 1990 can be described by an exponential function where the formula given is P(n) = 2000(1.02)ⁿ. This function reveals how the population size changes with each passing year.
The base of the exponent, 1.02, indicates the town's yearly percentage increase in population. To find the percentage growth rate, we simply subtract 1 from the base and multiply the result by 100. Therefore, the annual growth rate is ((1.02 - 1) × 100)%, which simplifies to 2%.
The exponential model given demonstrates that the population of the town grows at a constant percentage rate each year—in this case, a 2% increase per year. It's important to understand that exponential growth has profound implications over the long term, as it can lead to large population sizes. This type of growth is contrasted to logistic growth, which accounts for limiting factors and typically slows down as the population reaches a certain size.