https://file.aiquickdraw.com/mathbot/file/1727547881121tezqwyww.jpg

The problem describes the population of a town growing linearly. Here’s how to break it down:

1. **Initial population** in 2003 = 57,000
2. **Growth rate** per year = 2,200 people

### Part 1: Writing an equation for the population

The population growth is linear, which means the equation follows the form:

\[
P = P_0 + r \cdot x
\]

Where:
- \( P_0 \) is the initial population (57,000),
- \( r \) is the growth rate (2,200 per year),
- \( x \) is the number of years after 2003.

Thus, the equation becomes:

\[
P = 57,000 + 2,200x
\]

### Part 2: Finding the population in 2009

To find the population in 2009, we substitute \( x = 2009 - 2003 = 6 \) into the equation:

\[
P = 57,000 + 2,200 \cdot 6
\]

Now, I'll calculate the population in 2009.The population in 2009 is \( 70,200 \).

Would you like further details on this solution? Here are 5 related questions you might find helpful:

1. How would the population change in the year 2015?
2. Can you explain how linear growth differs from exponential growth?
3. What happens to the population if the growth rate changes to 3,000 people per year?
4. How can this linear model be applied to predict population in future years, such as 2025?
5. What is the slope of the population growth, and how does it affect the equation?

**Tip:** For linear growth, the slope (growth rate) directly affects how quickly the population increases over time.

A town's population has been growing linearly. In 2003, the population was 57,000. The population has been growing by 2,200 people each year. Write an equation for the population, P, x years after 2003. Use the formula to find the population in 2009.

Learn how to model population growth using a linear equation. This problem involves finding an equation for a town's population growing by 2,200 people per year and calculating the population in 2009. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation