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

## Activity: 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. ### Comment

You learned how to find percentages of numbers earlier. (a) There are two methods for finding percentages of numbers, shown on the calculator screens here:  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 .

Method 2 is a little quicker. If the population rises by 3.1%, then the new population is , 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. (b) Using the calculator to find 103.1% of 5,678, you get: Or: 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. ### Comment

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

For method 2, the new population is of the 2010 population. (c) Finding 24% of 820 on your calculator gives: So, the population drops by 197, and the predicted population in the year 2020 is then .

For method 2, the new population is of the 2010 population. Using the calculator to find 76% of 820: 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