To solve this, we need to analyze the population values as an arithmetic sequence.

Step 1: Verify that the population is in an arithmetic sequence

In an arithmetic sequence, the difference between consecutive terms is constant. Let's calculate the differences between each year:

1. Difference between 2011 and 2010: $5421 - 5000 = 421$

2. Difference between 2012 and 2011: $5836 - 5421 = 415$

3. Difference between 2013 and 2012: $6293 - 5836 = 457$

4. Difference between 2014 and 2013: $6725 - 6293 = 432$

5. Difference between 2015 and 2014: $7202 - 6725 = 477$

The differences are not exactly the same but are close. We can approximate the common difference by taking the average of these values:

$\text{Average difference} = \frac{421 + 415 + 457 + 432 + 477}{5} = \frac{2202}{5} = 440.4$

Step 2: Use the arithmetic sequence formula

The formula for the $n$-th term of an arithmetic sequence is:

$a_n = a_1 + (n - 1)d$

Where:

• $a_n$ is the population in year $n$,
• $a_1 = 5000$ (the population in 2010),
• $d = 440.4$ (the common difference),
• $n$ is the number of years after 2010.

Step 3: Predict the population in 2024

To find the population in 2024, we need $n = 2024 - 2010 = 14$.

Using the formula for the 14th term: $a_{14} = 5000 + (14 - 1) \times 440.4 = 5000 + 13 \times 440.4$ $a_{14} = 5000 + 5725.2 = 10725.2$

Thus, the predicted population in 2024 is approximately 10,700 (to three significant figures).

Would you like more details on this, or do you have any questions?

Related Questions:

1. How does an arithmetic sequence differ from a geometric sequence?
2. How can we estimate a more accurate common difference using statistical methods?
3. What are the limitations of using arithmetic sequences for population predictions?
4. How would the prediction change if we used a geometric model instead?
5. How does rounding affect predictions in sequences like this?

Tip:

When working with sequences, always check if the differences or ratios between terms are consistent before assuming the type of progression.