Question

a towns population has been growing linearly. in 2003 the population was 61,000. the population has been growing by 700 people each year. write an equation for the population, p, x years after 2003. p = use the formula to find the population in 2009: question help: video submit question

Explanation:

Part 1: Writing the Population Equation

Step 1: Recall linear growth formula

The general form of a linear equation is \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value). In the context of population growth, if \( P \) is the population \( x \) years after 2003, the initial population (when \( x = 0 \), i.e., in 2003) \( b=61000 \), and the rate of growth \( m = 700 \) (since the population grows by 700 people each year).
So the equation for the population \( P \) in terms of \( x \) (years after 2003) is \( P=700x + 61000 \).

Part 2: Finding the Population in 2009

Step 1: Calculate the number of years after 2003

To find the population in 2009, we first find the value of \( x \). Since 2009 - 2003=6, \( x = 6 \).

Step 2: Substitute \( x = 6 \) into the population equation

We use the equation \( P = 700x+61000 \). Substitute \( x = 6 \) into the equation:
\( P=700\times6 + 61000 \)
First, calculate \( 700\times6=4200 \).
Then, add this to 61000: \( P=4200 + 61000=65200 \).

Answer:

The equation for the population is \( P = 700x + 61000 \). The population in 2009 is 65200.