Final answer:
Scoville exhibits linear growth, increasing its population by 318 each year, leading to a projected population of 1,518 in three years. Oak Forest exhibits exponential growth, growing by 3% annually, resulting in a projected population of approximately 45,692 in three years.
Step-by-step explanation:
When distinguishing between linear and exponential growth in populations, the key factor is how the size of the population changes over time. For the population of Scoville, which is increasing at a consistent rate of 318 people per year, this represents linear growth. Linear growth suggests that the change in population size is constant every year, regardless of the current population. Therefore, to calculate the population in three years, we must multiply the rate of growth (318) by the number of years (3) and then add this number (954) to the current population (564), which results in a future population of 1,518.
In contrast, the population of Oak Forest is increasing by a rate of 3% per year, which qualifies as exponential growth. With exponential growth, the change in population size is proportional to its current size, meaning it grows more rapidly as the population increases. To calculate the population after three years with a 3% annual growth rate, we apply the formula P = P0 (1 + r)^t, where P0 is the current population (41,826), r is the growth rate (0.03), and t is the number of years (3). The calculation yields a future population of approximately 45,691.6, which rounds to 45,692.