- The initial population in 1683 is \(30,000,000\).
- Subtracting the decrease of \(23,000,000\) gives a target population of \(7,000,000\), which corresponds to the year \(1831\) in the table.
- The percentage decline is calculated as \(\left(\frac{23,000,000}{30,000,000}\right) \times 100\% \approx 76.67\%\).
- The final answers are the year \(\boxed{1831}\) and the percentage \(\boxed{76.67\%}\).
Explanation
- Problem Analysis and Identifying the Year
The data provided shows the population of the Ottoman Empire for five specific years: 1520, 1566, 1683, 1831, and 1856. We are asked to identify the year after 1683 where the population decreased by about 23,000,000 and to determine the percentage decline from the 1683 population.
- The population in 1683 was 30,000,000.
- A decrease of approximately 23,000,000 leads to a target population of \(30,000,000 - 23,000,000 = 7,000,000\).
- Comparing this to the table, the population in 1831 was 7,230,660, which is very close to the target of 7,000,000. Therefore, the year in question is 1831.
- Calculating the Percentage Decline
To find the percentage decline, we use the initial population in 1683 and the actual amount of decrease.
- The decrease is \(23,000,000\).
- The initial population in 1683 is \(30,000,000\).
- The percentage decline is calculated by dividing the decrease by the initial population and multiplying by \(100\%\):
\[\text{Percentage Decline} = \left(\frac{23,000,000}{30,000,000}\right) \times 100\% = \frac{23}{30} \times 100\% \approx 76.67\%\]
Thus, the population decrease represents a decline of approximately \(76.67\%\).
Examples
Calculating percentage changes is a vital skill for historical analysis, economics, and business. For example, if a company's revenue drops from \$\$30 million to \$\$7.23 million, managers use the same percentage decline formula to assess performance and identify periods of significant downturn. This helps in understanding trends, planning for recovery, and making data-driven decisions for the future. Understanding such changes allows one to compare historical growth or decline across different time periods effectively.