To project the population from 2024 to 2034 using the arithmetic, geometric, and exponential growth models, we need to understand and apply the formulas for each model.

Given Data:

• Population in 2006: $P_{2006} = 184,389$
• Population in 2022 (Projected): $P_{2022} = 266,200$
• Annual growth rate: $r = 2.3\%$

1. Arithmetic Growth Model

In an arithmetic growth model, the population increases by a constant amount each year. This constant amount can be found using:

$\Delta P = \frac{P_{2022} - P_{2006}}{2022 - 2006}$

$\Delta P = \frac{266,200 - 184,389}{16} = \frac{81,811}{16} \approx 5,113.19$

Thus, the population each year increases by 5,113.19.

The population in year $t$ (starting from 2024) is given by:

$P(t) = P_{2024} + (t - 2024) \times \Delta P$

We first calculate $P_{2024}$:

$P_{2024} = P_{2022} + 2 \times \Delta P = 266,200 + 2 \times 5,113.19 = 276,426.38$

Using this, the population for any year $t$ between 2024 and 2034 can be calculated as:

$P(t) = 276,426.38 + (t - 2024) \times 5,113.19$

2. Geometric Growth Model

In a geometric growth model, the population increases by a constant percentage each year. The population at year $t$ is given by:

$P(t) = P_{2024} \times (1 + r)^{t - 2024}$

where $r = 0.023$ (2.3%).

Using $P_{2024} = 276,426.38$:

$P(t) = 276,426.38 \times (1.023)^{t - 2024}$

3. Exponential Growth Model

In an exponential growth model, the population grows continuously at a constant rate $r$. The population at year $t$ is given by:

$P(t) = P_{2024} \times e^{r \times (t - 2024)}$

where $e$ is the base of the natural logarithm.

Using $P_{2024} = 276,426.38$ and $r = 0.023$:

$P(t) = 276,426.38 \times e^{0.023 \times (t - 2024)}$

Summary

You can now calculate the population from 2024 to 2034 using these formulas. For a specific year, just substitute $t$ with that year.

Would you like me to calculate the specific population for each year from 2024 to 2034 using these models?

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Here are some related questions:

1. How does the population growth compare between the three models for the same time period?
2. What are the implications of using different growth models in population projections?
3. How would the projections differ with a lower or higher growth rate?
4. What would happen if we included migration factors in these projections?
5. How does the choice of base year (e.g., 2006 vs. 2022) affect the long-term projection?

Tip: When modeling population growth, always consider which model best fits historical data and current trends to avoid overestimating or underestimating future populations.