As your eye shows, the rate of increase in population is slowing a bit over time. Here's a figure breaking down the average population growth rates for the world and by by region. For the world, population growth rates are projected to fall from 2% in 1970 to 0.5% by 2050. For Europe, population growth rates are at zero percent now, and slated to fall lower. A number of other regions are headed that way as well, with population growth in Africa the clear outlier. The report notes: "[T]the annual increase in that populationhas been declining since the late 1960s. By 2050, it is expected that the world’s population will be growing by 49 million people per year, more than half of whom will live in the least developed countries. Currently, of the 82 million people added to the world’s population every year, 54 per cent are in Asia and 33 per cent in Africa. By 2050, however, more than 80 per cent of the global increase will take place in Africa, with only 12 per cent in Asia."
These lower rates of population growth are reflected in lower fertility rates. Back in 1970, only Europe and Northern America had fewer than three births per woman. Now the world average is less than three births per woman, although Africa's rate remains higher. Still, Africa's birthrate per woman roughly matches where Latin America and Asia were in the late 1970s, and fertility rates can in some cases shift quite rapidly.
People are living longer. For the world as a whole, life expectancies are up from less than 60 years in 1970 to about 70 years now. The disparity in life expectancies is much smaller than the disparity in incomes. A person in a high-income country may have 10 or 20 times as much income as someone in a low-income country, but they don't live 10 or 20 times longer.
Indeed, much of the remaining disparity in life expectancy happens not in old age, but among children. For the world as a while, about one child in every five died before reaching the age of 5 back in the 1950s. Now, only about one child in 20 dies before reaching the age of five. Even in Africa, the under-5 infant mortality rate has dropped to what the world average was as recently as the early 1980s.
These figures are all telling us something about how the typical or common life experience of a member of the human race is changing over time. In many countries of the world, population may move to different locations, but population is growing by little or nothing. Nuclear families are smaller. Women are spending less time pregnant, but when children are born, the parents are far less likely to face the tragedy of an early death (which of course could make such tragedies feel even more painful when they do occur). With longer life expectancies and smaller families, a giant family reunion in modern times is less likely to have a few older people and a swarm of children than the equivalent event a few decades ago. Instead, the attendees at that giant family reunion may be distributed fairly evenly across four generations. In these and other ways, our fundamental feelings about what seems usual and common in our families and communities is fundamentally different from previous generations of the human race.