Final answer:
The projected population of the town will be approximately 24,500 in 3 years, using the exponential growth formula based on the given doubling time of 28 months from an initial population of 10,000.
Step-by-step explanation:
The subject of this question is Mathematics, and it concerns itself with exponential growth. Given that the population doubled over 28 months, we can assume this growth rate is consistent. The current population is 10,000, and we want to calculate what the population will be in 3 years (36 months). Since 28 months is the doubling time, there will be one full doubling period plus a fraction of the next doubling period in those 3 years.
First, we find the number of doublings in 36 months by dividing 36 by 28, which is approximately 1.2857. Since the population doubles with each increment of 1, we can use the power of 2 to calculate the growth factor for the fractional doubling period beyond the first. Therefore, the projected population P in 3 years will be:
P = 10,000 × 21.2857
Calculating 2 to the power of 1.2857 gives us approximately 2.45. Hence, the population after 3 years is estimated to be:
P = 10,000 × 2.45
P ≈ 24,500
So, the projected population of the town in 3 years from now will be approximately 24,500.