To find the population of the city 12 years from now, we need to understand the concept of exponential growth, specifically how populations double over a given period.
### Step-by-Step Solution:
1. Understand the Problem:
- Current population: 538,000 people
- Doubling time: 6 years
- Time period of interest: 12 years
2. Determine How Many Doublings Occur:
- Since the population doubles every 6 years, we need to find out how many 6-year periods fit into 12 years:
[tex]\[
\text{Number of doublings} = \frac{\text{Time period of interest}}{\text{Doubling time}} = \frac{12 \text{ years}}{6 \text{ years}} = 2 \text{ doublings}
\][/tex]
3. Calculate the Population After Each Doubling:
- The population doubles twice over 12 years.
- Initial population: 538,000
- After the first doubling (6 years):
[tex]\[
\text{Population} = 538,000 \times 2 = 1,076,000
\][/tex]
- After the second doubling (another 6 years, total 12 years):
[tex]\[
\text{Population} = 1,076,000 \times 2 = 2,152,000
\][/tex]
4. Conclusion:
- The population 12 years from now will be 2,152,000 people.
### Final Answer:
[tex]\[
\boxed{2,152,000 \text{ people}}
\][/tex]
