Final answer:
It will take 10 years for the population of the small town to reach 1,000 people.
Step-by-step explanation:
To find out how many years it will take for the population of the small town to reach 1,000 people, we need to calculate the number of doubling times. The town currently has 3,000 people and we want to reach 1,000, so we need to know how many times the population needs to halve to reach that number.
Since the population doubles every 10 years, it will halve every 10 years as well. So, we can divide the difference in population (3,000 - 1,000 = 2,000) by the rate of halving (2,000 / 2 = 1,000) to get the number of doubling times. In this case, it will take 10 doubling times for the population to reach 1,000 people.
Therefore, it will take 10 years for the population to reach 1,000 people in the small town.