8.3.1 Percent Increase/Decrease

Let’s take another look at percentages. In the following exploration, you will use the calculator to find a percent increase and a percent decrease.

Calculator icon The calculator can be accessed on the left-hand side bar under Toolkit.

Activity symbolActivity: Island Population

The population of an island was 5,678 in the year 2010, with a prediction that it will rise by 3.1% over the next ten years (from 2010 to 2020). What will the population be in 2020?

There are two ways you can look at this calculation. For the first method, you find the increase and add it to the original population, and for the second, you find the new population as a percentage of the original one.

Method 1 involves finding 3.1% of the 2010 population of 5,678, then adding it to 5,678 to find the population in the year 2020.

(a) Find 3.1% of 5,678, and then find the predicted population of the island in the year 2020.

Hint symbol

Comment

You learned how to find percentages of numbers earlier.

Solution symbol

Answer

(a) There are two methods for finding percentages of numbers, shown on the calculator screens here:

Sum showing 3.1 over 100 in parenthesis multiplied by 5678 equals 17 and 9 five hundredths equals 176.018
Sum showing 3.1 percent multiplied by 5678 equals 176.018

3.1% of 5,678 is 176. You need to round to a whole number because you can only have a whole number of people!

The predicted population of the island in the year 2020 is five comma 678 plus 176 equals five comma 854.

Method 2 is a little quicker. If the population rises by 3.1%, then the new population is 100 percent prefix plus of 3.1 percent, or 103.1% of the 2010 population. The population in 2020 is therefore 103.1% of 5,678.

(b) Use this method to find the new population.

Solution symbol

Answer

(b) Using the calculator to find 103.1% of 5,678, you get:

Calculator screen showing 103.1 over 100 in parenthesis multiplied by 5678 = 5854 and nine five hundredths = 5854

Or:

103.1 percent multiplied by 5678 equals 5854.018

In the first screenshot, the calculator cuts off the end of the answer, but the full answer is shown in the white screen below it.

This method gives the same answer: The population of the island in 2020 is predicted to be 5,854.

Now you try a percent calculation, a percent decrease this time.

(c) The population on a neighboring island is falling. In the year 2010, it was 820, with a drop of 24% predicted over the next ten years (from 2010 to 2020). What will the population be in the year 2020? Try both methods shown above and make sure that they give the same answer.

Hint symbol

Comment

For method 1, find 24% of 820, and then subtract it from 820.

For method 2, the new population is 100 percent negative 24 percent of the 2010 population.

Solution symbol

Answer

(c) Finding 24% of 820 on your calculator gives:

Two separate sums, one on left showing 24 over 100 in parenthesis multiplied by 820 equals 196 and four fifths equals 196.8 the sum on the right showing 24 percent multiplied by 820 equals 196.8

So, the population drops by 197, and the predicted population in the year 2020 is then 820 minus 197 equals 623.

For method 2, the new population is 100 percent negative 24 percent equals 76 percent of the 2010 population. Using the calculator to find 76% of 820:

Two separate sums, one on left showing 76 over 100 in parenthesis multiplied by 820 equals 623 and one fifth equals 623.2 and the one on the right showing 76 percent multiplied by 820 equals 623.2

The predicted population in the year 2020 is 623.

To recap:

To find the new amount after a percent increase, either:

  • find the increase and add it to the original amount, or
  • write the new amount as 100% plus the % increase, and find this percentage.

To find the new amount after a percent decrease, either:

  • find the decrease and subtract it from the original amount, or
  • write the new amount as 100% minus the % decrease, and find this percentage.

Now you can use your calculator for future percentage calculations.

8.3 Extensions and Further Exploration

8.3.2 Percent Decrease