Answer :
Sure! Let's go through the steps to determine whether the percentage increase in the South African population from 2011 to 2022 is correct.
1. Identify the Initial and Final Populations:
- Initial population in 2011: 51.7 million
- Final population in 2022: 62.0 million
2. Calculate the Increase in Population:
- Increase = Final population - Initial population
- Increase = 62.0 million - 51.7 million
- Increase = 10.3 million
3. Calculate the Percentage Increase:
- Percentage increase is calculated using the formula:
[tex]\[
\text{Percentage Increase} = \left(\frac{\text{Increase}}{\text{Initial Population}}\right) \times 100
\][/tex]
- Substituting the known values:
[tex]\[
\text{Percentage Increase} = \left(\frac{10.3}{51.7}\right) \times 100 \approx 19.92\%
\][/tex]
4. Compare the Calculated Percentage to the Given Percentage:
- The calculated percentage increase is approximately 19.92%.
- The given percentage increase in the problem is 19.8%.
5. Determine Accuracy:
- Since 19.92% is not the same as 19.8%, the calculated percentage increase is not exactly equal to the given percentage increase.
Therefore, based on these calculations, the actual percentage increase in the population is about 19.92%, which indicates that the given percentage of 19.8% is slightly off. The percentage increase is not correct.
1. Identify the Initial and Final Populations:
- Initial population in 2011: 51.7 million
- Final population in 2022: 62.0 million
2. Calculate the Increase in Population:
- Increase = Final population - Initial population
- Increase = 62.0 million - 51.7 million
- Increase = 10.3 million
3. Calculate the Percentage Increase:
- Percentage increase is calculated using the formula:
[tex]\[
\text{Percentage Increase} = \left(\frac{\text{Increase}}{\text{Initial Population}}\right) \times 100
\][/tex]
- Substituting the known values:
[tex]\[
\text{Percentage Increase} = \left(\frac{10.3}{51.7}\right) \times 100 \approx 19.92\%
\][/tex]
4. Compare the Calculated Percentage to the Given Percentage:
- The calculated percentage increase is approximately 19.92%.
- The given percentage increase in the problem is 19.8%.
5. Determine Accuracy:
- Since 19.92% is not the same as 19.8%, the calculated percentage increase is not exactly equal to the given percentage increase.
Therefore, based on these calculations, the actual percentage increase in the population is about 19.92%, which indicates that the given percentage of 19.8% is slightly off. The percentage increase is not correct.
