Problem

A town's population has been growing linearly. In 2003 the population was 63,000 . The population has been growing by 1700 people each year. Write an equation for the population, P, $x$ years after 2003. \[ P= \] Use the formula to find the population in 2009:

Solution

Step 1 :The population growth is linear, which means it can be represented by the equation of a straight line, y = mx + c, where m is the slope (rate of growth) and c is the y-intercept (initial population). In this case, the slope is 1700 (the number of people the population grows by each year) and the y-intercept is 63,000 (the population in 2003). The variable x represents the number of years after 2003.

Step 2 :To find the population in 2009, we need to substitute x = 2009 - 2003 = 6 into the equation.

Step 3 :\(P = 1700x + 63000\)

Step 4 :\(P = 1700*6 + 63000\)

Step 5 :\(P = 10200 + 63000\)

Step 6 :\(P = 73200\)

Step 7 :Final Answer: The equation for the population, P, $x$ years after 2003 is \(P = 1700x + 63000\). The population in 2009 was \(\boxed{73200}\).

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Source: https://solvelyapp.com/problems/25291/

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