2006= 184389
2.3% annual population change. Using The arithmetic geometric and exponential growth model project from 2024-2034

To project the population from 2024 to 2034 using different growth models—arithmetic, geometric, and exponential—based on a 2.3% annual population change rate, we'll calculate the expected population for each year under each model. The initial population in 2024 is assumed to be \( P_0 = 184,389 \).

### 1. **Arithmetic Growth Model:**
In an arithmetic growth model, the population increases by a constant absolute amount each year. This amount is derived from the initial population growth rate.

- **Annual Growth Amount**: 
  \[
  \Delta P = P_0 \times \frac{2.3}{100} = 184,389 \times 0.023 = 4,240.947
  \]

- **Population in Year \( n \)** (where \( n \) is the number of years after 2024):
  \[
  P(n) = P_0 + n \times \Delta P
  \]

### 2. **Geometric Growth Model:**
In a geometric growth model, the population increases by a constant percentage each year. 

- **Annual Growth Factor**:
  \[
  r = 1 + \frac{2.3}{100} = 1.023
  \]

- **Population in Year \( n \)**:
  \[
  P(n) = P_0 \times r^n
  \]

### 3. **Exponential Growth Model:**
In an exponential growth model, the population grows continuously at a constant rate. 

- **Exponential Growth Formula**:
  \[
  P(t) = P_0 \times e^{rt}
  \]
  where \( r = \frac{2.3}{100} = 0.023 \) and \( t \) is the number of years after 2024.

Let's compute the projected populations for each year from 2024 to 2034 under each model.

### Projected Population Calculations:

I'll calculate the populations using the formulas above.Here are the projected populations for each year from 2024 to 2034 using the arithmetic, geometric, and exponential growth models:

| Year | Arithmetic Growth | Geometric Growth | Exponential Growth |
|------|-------------------|------------------|--------------------|
| 2024 | 184,389           | 184,389          | 184,389            |
| 2025 | 188,629           | 188,629          | 188,679            |
| 2026 | 192,871           | 192,968          | 193,069            |
| 2027 | 197,112           | 197,407          | 197,561            |
| 2028 | 201,353           | 201,947          | 202,158            |
| 2029 | 205,594           | 206,592          | 206,861            |
| 2030 | 209,835           | 211,343          | 211,674            |
| 2031 | 214,076           | 216,204          | 216,599            |
| 2032 | 218,317           | 221,177          | 221,638            |
| 2033 | 222,558           | 226,264          | 226,795            |
| 2034 | 226,798           | 231,468          | 232,072            |

### Summary:
- **Arithmetic Growth**: Adds a constant population increase of approximately 4,241 each year.
- **Geometric Growth**: Multiplies the population by a constant factor of 1.023 each year.
- **Exponential Growth**: Assumes continuous growth, leading to slightly higher population estimates compared to the geometric model by 2034.

Would you like more details or have any questions?

### Related Questions:
1. How do the different models affect long-term population projections?
2. What are the implications of using an arithmetic model versus a geometric or exponential model for planning purposes?
3. How does the choice of growth model impact resource allocation in urban planning?
4. Can you explain the significance of the growth rate in each model?
5. How would a change in the growth rate (e.g., from 2.3% to 3%) affect the projections?

**Tip**: Always consider the nature of the system (linear vs. exponential) when choosing a growth model for predictions.

Explore how arithmetic, geometric, and exponential growth models project population changes from 2024 to 2034. Detailed analysis includes calculations based on a 2.3% annual population change rate.

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