Section Warm-Up
Suppose you live in a town that has a population of 1,000 people and the population is increasing at a rate of 5% each year. You want to find out how many people will live in your town in 5 years. Let’s work though the process of finding this solution one step at a time.
The first step is to convert 5% into a decimal.
Year 2009: 1,000
Multiply the original population by the rate of change.
Year 2010: 1,000(.05) = 50
50 is the increase in population for the year. This means that the final population for the year 2010 is 1,050. Let’s repeat this process for 2011. Remember, the new starting population is 1,050 not 1,000.
2011: 1,050(.05) = 52.5 + 1050 = 1,102.5
Continue on for the next three years.
2012: 1,102.5(.05) = 55.125 + 1,102.5 = 1,157.625
2013: 1,157.625(.05) = 57.88125 + 1157.625 = 1,215.50625
2014: 1,215.50625(.05) = 60.7753125 + 1,215.50625 = 1,276.28156
These computations were made to many decimal places but we can round to the nearest whole number since you can’t have .28 of a person. In 2014 the population will be approximately 1,276 people.
This process would be very cumbersome if we needed to continue for any more years. Keep reading this section to find out a shortcut for this process.