2.3 The South African population grew by 19.8% between 2011 and 2022, from 51.7 million to 62 million. Show by means of calculations whether the percentage increase is correct or not. (3 points)

2.4 It is projected that the South African population will increase by 17.045% from 2022 to 2030. Determine the projected South African population in 2030. (3 points)

Let's solve the question step by step.

### Part 1: Verify the Percentage Increase from 2011 to 2022

Given:
- Population in 2011: 51.7 million
- Population in 2022: 62 million
- Stated increase: 19.8%

First, we calculate the percentage increase using the formula:

[tex]\[ \text{Percentage Increase} = \left( \frac{\text{New Population} - \text{Old Population}}{\text{Old Population}} \right) \times 100 \][/tex]

Plug in the given values:

[tex]\[ \text{Percentage Increase} = \left( \frac{62 - 51.7}{51.7} \right) \times 100 \][/tex]

Perform the calculations:

[tex]\[ \text{Percentage Increase} = \left( \frac{10.3}{51.7} \right) \times 100 \approx 19.92\% \][/tex]

The calculated percentage increase is approximately 19.92%, which is slightly different from the stated 19.8%. Therefore, the statement that the population grew by 19.8% is not correct.

### Part 2: Projected Population in 2030

Given:
- Population in 2022: 62 million
- Projected increase from 2022 to 2030: 17.045%

To find the projected population, use the formula:

[tex]\[ \text{Projected Population} = \text{Current Population} \times \left(1 + \frac{\text{Projected Increase Percentage}}{100}\right) \][/tex]

Plug in the given values:

[tex]\[ \text{Projected Population} = 62 \times \left(1 + \frac{17.045}{100}\right) \][/tex]

Perform the calculations:

[tex]\[ \text{Projected Population} = 62 \times 1.17045 \approx 72.57 \, \text{million} \][/tex]

The projected South African population in 2030 is approximately 72.57 million.