Answer :
To find the equation for a town's population based on its growth, we need to understand that the population increases by a fixed number of people each year. This kind of growth is described as linear growth.
Here's how you can determine the equation:
1. Identify the initial population: In 2003, the town's population was 29,000 people. This will be our starting point, or base population, for the equation.
2. Determine the annual growth: The population has been increasing by 1,700 people each year. This is the rate of growth per year.
3. Write the equation:
- Let [tex]\( x \)[/tex] represent the number of years after 2003.
- The population in any year [tex]\( x \)[/tex] years after 2003 can be determined by adding the initial population to the product of the number of years and the annual growth rate.
- Using this information, the equation for the population, [tex]\( P(x) \)[/tex], is:
[tex]\[
P(x) = 29000 + 1700 \times x
\][/tex]
This equation allows you to calculate the town's population for any year after 2003 by substituting [tex]\( x \)[/tex] with the number of years since then.
Here's how you can determine the equation:
1. Identify the initial population: In 2003, the town's population was 29,000 people. This will be our starting point, or base population, for the equation.
2. Determine the annual growth: The population has been increasing by 1,700 people each year. This is the rate of growth per year.
3. Write the equation:
- Let [tex]\( x \)[/tex] represent the number of years after 2003.
- The population in any year [tex]\( x \)[/tex] years after 2003 can be determined by adding the initial population to the product of the number of years and the annual growth rate.
- Using this information, the equation for the population, [tex]\( P(x) \)[/tex], is:
[tex]\[
P(x) = 29000 + 1700 \times x
\][/tex]
This equation allows you to calculate the town's population for any year after 2003 by substituting [tex]\( x \)[/tex] with the number of years since then.
