Question

analyze is it possible to have a percent of increase of more than 100%? is it possible to have a percent of decrease of more than 100%? explain.

Explanation:

For percent increase over 100%:

The formula for percent increase is \(\text{Percent Increase}=\frac{\text{New Amount}-\text{Original Amount}}{\text{Original Amount}}\times100\%\). If the new amount is more than double the original (e.g., original = 10, new = 30), then \(\frac{30 - 10}{10}\times100\%=200\%\), so over 100% is possible.

For percent decrease over 100%:

The formula for percent decrease is \(\text{Percent Decrease}=\frac{\text{Original Amount}-\text{New Amount}}{\text{Original Amount}}\times100\%\). The new amount can't be negative (since it represents a quantity like number of items, weight, etc.). The minimum new amount is 0, so \(\frac{\text{Original}-0}{\text{Original}}\times100\% = 100\%\). Thus, a decrease over 100% is impossible as it would require the new amount to be negative, which doesn't make sense for most real - world quantities we measure with percent decrease.

Answer:

• It is possible to have a percent of increase of more than 100%. For example, if the original amount is 5 and the new amount is 15, the percent increase is \(\frac{15 - 5}{5}\times100\%=200\%\), which is more than 100%.
• It is not possible to have a percent of decrease of more than 100%. The formula for percent decrease is \(\frac{\text{Original}-\text{New}}{\text{Original}}\times100\%\). The new amount cannot be negative (for most real - world quantities we use percent decrease for, like number of objects, weight, etc.). The lowest the new amount can be is 0, and when the new amount is 0, the percent decrease is \(\frac{\text{Original}-0}{\text{Original}}\times100\% = 100\%\). So we can't have a percent decrease greater than 100% as it would imply the new amount is negative, which is not meaningful in most cases.