Question

In a small town with a population of 50,000 losing about 3% of people per year due to its proximity to a new highway, what is the estimated population after 5 years?

a. 45,000
b. 46,344
c. 47,625
d. Not specified

Answer 1

The estimated population of the small town after 5 years is approximately 46,344.

Step-by-step explanation:

To estimate the population of the small town after 5 years, we can use the formula: population = initial population * (1 - growth rate)^number of years. In this case, the initial population is 50,000 and the growth rate is 3% per year, which means the town is losing 3% of its population each year. So the formula becomes: population = 50,000 * (1 - 0.03)^5. Simplifying this calculation gives us approximately 46,344, so the estimated population after 5 years is 46,344 (option b).

Answer 2

Final answer:

The estimated population after 5 years would be approximately 43,154.

Step-by-step explanation:

To calculate the estimated population after 5 years, we need to find the population decrease each year. If the town is losing about 3% of its population per year, the remaining population will be 97% of the previous year's population. So, the population after the first year would be 50,000 * 0.97 = 48,500.

Similarly, the population after the second year would be 48,500 * 0.97 = 47,045. Continuing this pattern, we can calculate the population after 5 years:

1. Year 1: 50,000 * 0.97 = 48,500
2. Year 2: 48,500 * 0.97 = 47,045
3. Year 3: 47,045 * 0.97 = 45,678
4. Year 4: 45,678 * 0.97 = 44,384
5. Year 5: 44,384 * 0.97 = 43,154

Therefore, the estimated population after 5 years would be approximately 43,154