Consider this scenario: A town's population has been decreasing at a constant rate. In 2010 the population was 5,200. By 2013 the population had dropped to 4,300. Assume this trend continues.

Identify the year in which the population will reach 0. (Round your answer down to the nearest year.)

To solve the problem, we first need to determine the rate at which the population is decreasing per year. 

### Step 1: Find the rate of decrease per year
The population in 2010 was 5,200, and by 2013 it had decreased to 4,300. The number of years between 2010 and 2013 is:

\[
2013 - 2010 = 3 \text{ years}
\]

The decrease in population over these 3 years is:

\[
5,200 - 4,300 = 900 \text{ people}
\]

The rate of decrease per year is:

\[
\frac{900 \text{ people}}{3 \text{ years}} = 300 \text{ people per year}
\]

### Step 2: Determine when the population will reach 0
To find when the population will reach 0, we use the initial population (5,200 people) and the rate of decrease (300 people per year). We set up the equation:

\[
\text{Population} = 5200 - 300 \times t
\]

where \( t \) is the number of years after 2010.

We need to find \( t \) when the population reaches 0:

\[
5200 - 300t = 0
\]

Solve for \( t \):

\[
300t = 5200
\]

\[
t = \frac{5200}{300} \approx 17.33 \text{ years}
\]

### Step 3: Determine the exact year
Since \( t \) is the number of years after 2010, we add 17 years to 2010:

\[
2010 + 17 = 2027
\]

Since the problem asks us to round down to the nearest year, the population will reach 0 in **2027**.

---

Would you like more details on any of the steps or have any questions? Here are some related questions to consider:

1. What would be the population in 2020 if the trend continues?
2. How would the model change if the population decrease rate was not constant?
3. Can the rate of population decrease be expressed as a percentage per year?
4. How would an external factor causing a sudden decrease in population affect this prediction?
5. If the population decreases by a fixed percentage instead of a fixed amount, when would it reach 0?

**Tip:** When working with linear models like this, always check the rate of change and ensure it matches the context of the problem.

Consider this scenario: A town's population has been decreasing at a constant rate. In 2010 the population was 5,200. By 2013 the population had dropped to 4,300. Assume this trend continues. Identify the year in which the population will reach 0. (Round your answer down to the nearest year.)

Determine the year in which a town's population will reach zero, given a constant rate of decrease. This problem involves linear equations and the concept of rate of change, ideal for students in Grades 6-8. The solution explains step-by-step how to calculate the year based on a given initial population and annual decrease rate.

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