To calculate the projected population for each year using the arithmetic growth method, we'll use the formula provided:

$\text{Projected Population} = \left(\frac{\text{GR}}{100} \times P_1\right) + P_1$

Where:

• $P_1$ = Initial Population (184,389)
• GR = Growth Rate (2.3%)

Step-by-Step Calculation

1. Calculate the increase in population for the first year (2006):

$\text{Increase} = \left(\frac{2.3}{100} \times 184,389\right)$

2. Add this increase to the initial population to get the population for the next year (2007):

$P_2 = \text{Increase} + P_1$

3. Repeat this process for each subsequent year until 2034.

Let’s calculate the population for 2007 as an example.

Calculation for 2007:

1. Increase in population:

$\text{Increase} = \frac{2.3}{100} \times 184,389 = 4,240.95$

2. Population for 2007:

$P_2 = 184,389 + 4,240.95 = 188,629.95 \approx 188,630$

General Formula

If you want to calculate for a specific year $t$ years after 2006, you can use:

$P_t = P_1 \times \left(1 + \frac{\text{GR}}{100}\right)^t$

For a more accurate projection over multiple years, we typically use the compound interest method. However, since you asked for the arithmetic method, we will stick to adding the same amount each year.

Do you want detailed calculations for every year until 2034, or would you like a specific year's population projection?

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Relative Questions:

1. How does the arithmetic growth model differ from the geometric (compound) growth model?
2. What factors could cause deviations from this projected population growth in real life?
3. How would a decrease in the growth rate affect the projections?
4. What could be the implications of this population growth for the local government area?
5. How would you adjust the formula if the growth rate changes after a certain year?

Tip: When projecting populations or any other metric over a long period, consider multiple growth models to understand the possible range of outcomes.