2.4 billion is not correct.
In order for Africa to have its population reach 2.4 billion by 2100, the continent’s high fertility rates, which currently average five children per woman, would need to fall relatively rapidly. The declines in fertility would need to be at least as rapid as the fall in mortality rates that have occurred in most of Africa, where average life expectancy at birth has increased from 38 years to 56 years over the last half century.
Under the United Nations Population Division’s “low variant” population projection, the replacement level of two children per woman would be achieved in about 50 years. Fertility would continue to decline thereafter, reaching 1.65 children per woman by 2100. As a result of falling below replacement fertility, Africa’s population, having peaked at close to 2.4 billion, would begin its decline at the close of the century.
3.6 billion is not correct.
The UN "medium variant" projection assumes moderate declines in current fertility levels — that is, nearly halving by 2050 and achieving the replacement level of approximately two children per woman by 2100. Achieving such a decline in fertility would entail sustained developmental progress, in particular educating the growing numbers of youth (especially girls), expanding women’s employment opportunities and providing family planning information and methods.
On that basis, Africa is projected to have a population of 3.6 billion people at the close of the century, representing 35% of the projected world population of 10.1 billion.
5.2 billion is not correct.
If fertility rates in Africa were to decline only relatively slowly, reaching a half child above the replacement level by 2100 (the UN's "high variant" projection), Africa's population would increase five-fold by the end of the century, to 5.2 billion.
Moreover, Africa would continue growing — adding nearly 60 million people annually at the start of the 22nd century, which is equal to the current population of Italy.
15 billion is correct.
Assuming the fertility rates of Africa’s 55 nations remain unchanged at their current levels, the population of Africa at the end of the 21st century would be an incredible 15 billion, which is more than double the current world population.
However, such an outcome is viewed as extremely improbable. Given current environmental concerns and resource constraints in many African nations, especially with respect to climate change and water shortages, it is clear the continent could not sustain a population anywhere near this large.