To estimate the population of a city for the years 2070, 2072, and 2100 AD using the incremental increase method, let's follow these steps:
### Step-by-Step Solution
Step 1: Identify the given census data
The census data includes the population counts for specific years:
- Year 2000: 11,000 people
- Year 2010: 30,000 people
- Year 2020: 50,000 people
- Year 2030: 90,000 people
- Year 2040: 120,000 people
- Year 2050: 135,000 people
Step 2: Calculate the incremental increases
To find the incremental increase in population between each decade:
- 2010 - 2000 = 30,000 - 11,000 = 19,000 people
- 2020 - 2010 = 50,000 - 30,000 = 20,000 people
- 2030 - 2020 = 90,000 - 50,000 = 40,000 people
- 2040 - 2030 = 120,000 - 90,000 = 30,000 people
- 2050 - 2040 = 135,000 - 120,000 = 15,000 people
So, the incremental increases are: 19,000, 20,000, 40,000, 30,000, and 15,000 people respectively.
Step 3: Calculate the average incremental increase
To find the average incremental increase:
Average Incremental Increase = (19,000 + 20,000 + 40,000 + 30,000 + 15,000) / 5 = 124,000 / 5 = 24,800 people per decade.
Step 4: Estimate the future populations
Based on the average incremental increase, estimate the populations for future years:
1. For the year 2070:
- Years to add = 2070 - 2050 = 20 years
- Population increase = (24,800 / 10) 20 = 49,600 people
- Estimated Population for 2070 = 135,000 + 49,600 = 184,600 people
2. For the year 2072:
- Years to add = 2072 - 2050 = 22 years
- Population increase = (24,800 / 10) 22 = 54,560 people
- Estimated Population for 2072 = 135,000 + 54,560 = 189,560 people
3. For the year 2100:
- Years to add = 2100 - 2050 = 50 years
- Population increase = (24,800 / 10) * 50 = 124,000 people
- Estimated Population for 2100 = 135,000 + 124,000 = 259,000 people
Thus, the estimated populations of the city for the specified future years are:
- For 2070: 184,600 people
- For 2072: 189,560 people
- For 2100: 259,000 people
