A town's population has been growing linearly. In 2003 the population was 70,000.

Question

The population has been growing by 2200 people each year..                                                                                             Use the formula to find the population in 2009:  Please not only give both answers but please show me how you did this problem.

Answer 1

If a population grows linearly it means that it grows the exact same amount for every interval, in this case every year.

You're given that the population was 70,000 in 2003. This number is a constant because nothing can manipulate that number for that year. The number that will change the population every year is 2200 because that is how much the population increases every year. Therefore, the equation will be as follows:

70000 + 2200x = (population 'x' years after 2003)

For x you plug in the amount of years AFTER 2003. To see how this works plug in 0 for x. 0 means that we have not moved any years past 2003 so the population would be 70,000 which is what you are given. So 2009 is 6 years after 2003 so plug in 6 for x: 

70000 + 2200(6) = (population for 2009)

70000 + 13200 = 83200

So in 2009 the population is 83200 people.

 

To prove this works:

Population in 2003: 70000

Population in 2004: 70000 + 2200 = 72200

Population in 2005: 72200 + 2200 = 74400

Population in 2006: 74400 + 2200 = 76600

Population in 2007: 76600 + 2200 = 78800

Population in 2008: 78800 + 2200 = 81000

Population in 2009: 81000 + 2200 = 83200

 

Hope this helps!