a state with a population of 225672 in 2006, with an annual population change of 2.3% using arithemetic model of population projection, project their population form 2006 t0 2034 accordingly 

To project the population from 2006 to 2034 using the arithmetic model of population projection, we proceed as follows:

### Step 1: Understand the Arithmetic Growth Model
The arithmetic model assumes a constant absolute change in population every year. The population at any given year \( P(t) \) can be calculated using the formula:

\[
P(t) = P_0 + (t - t_0) \times d
\]

Where:
- \( P(t) \) is the population in year \( t \).
- \( P_0 \) is the initial population (in 2006).
- \( t_0 \) is the base year (2006).
- \( d \) is the annual absolute increase in population.

### Step 2: Calculate the Annual Absolute Increase (\( d \))
Given:
- Initial population \( P_0 = 225672 \) in 2006.
- Annual percentage change = 2.3%.

The absolute increase in population each year \( d \) is calculated as:

\[
d = \frac{2.3}{100} \times P_0 = \frac{2.3}{100} \times 225672 = 5180.456
\]

### Step 3: Project the Population for Each Year from 2006 to 2034
To find the population in 2034 (\( t = 2034 \)), we calculate:

\[
t - t_0 = 2034 - 2006 = 28 \text{ years}
\]

\[
P(2034) = P_0 + 28 \times d
\]

\[
P(2034) = 225672 + 28 \times 5180.456 = 225672 + 145052.768 = 370724.768
\]

Rounding to the nearest whole number, the projected population in 2034 is **370,725**.

### Final Answer
The projected population in 2034 is **370,725** using the arithmetic model of population projection.

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Would you like further details or have any questions? Here are some related questions:

1. How does the arithmetic model compare to the geometric model in population projection?
2. What are the limitations of using an arithmetic model for population projection?
3. How would a change in the percentage rate affect the projected population?
4. Can the arithmetic model be applied to other types of growth, such as economic or environmental data?
5. What are other models of population growth besides arithmetic and geometric?

**Tip:** The arithmetic model is simple and easy to calculate, but it may not accurately reflect real-world population dynamics, which often exhibit exponential or logistic growth patterns.

Learn how to project population growth using the arithmetic model of population projection. Calculate the population in 2034 starting from an initial population of 225,672 in 2006 with an annual growth rate of 2.3%. Discover the formula used and the step-by-step calculation process.

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