- The percentage increase for last year is calculated as \(\frac{10,000 - 5,000}{5,000} \times 100\% = \boxed{100\%}\).
- The percentage decrease for this year is calculated as \(\frac{10,000 - 5,000}{10,000} \times 100\% = \boxed{50\%}\).
Explanation
- Calculate Percentage Increase for Last Year
To determine the percentage increase for last year, we identify the initial sales value and the final sales value. The initial sales were \(I_1 = \$5,000\) and the final sales were \(F_1 = \$10,000\). The formula for percentage increase is given by \(\frac{F - I}{I} \times 100\%\). Substituting the values, we have \(\frac{10,000 - 5,000}{5,000} \times 100\% = \frac{5,000}{5,000} \times 100\% = 100\%\). Thus, sales increased by \(100\%\) last year.
- Calculate Percentage Decrease for This Year
To determine the percentage decrease for this year, we identify the initial sales value and the final sales value. The initial sales were \(I_2 = \$10,000\) and the final sales were \(F_2 = \$5,000\). The formula for percentage decrease is given by \(\frac{I - F}{I} \times 100\%\). Substituting the values, we have \(\frac{10,000 - 5,000}{10,000} \times 100\% = \frac{5,000}{10,000} \times 100\% = 0.5 \times 100\% = 50\%\). Thus, sales decreased by \(50\%\) this year.
Examples
Understanding percentage changes is essential in financial management and personal budgeting. For example, if a store tracks its revenue changes from month to month, calculating these percentages helps managers identify growth trends or periods where business performance slowed down. This allows for informed decision-making, such as adjusting marketing strategies during a sales dip or celebrating significant growth after a successful campaign.