For many, it’s a puzzling question: How can over 35 million Black Americans today trace their ancestry back to fewer than 450,000 African slaves who arrived in the U.S.?

The key to understanding this phenomenon is the principle of exponential growth. When a population experiences a constant rate of growth over time, it doesn’t merely increase incrementally; it grows at an accelerating pace. This assumes that the growth conditions, such as fertility rates, mortality rates, and migration, remain relatively consistent.

As the population grows, the number of people added in each generation increases. Furthermore, descendants of the African slave population include children born from mixed unions, contributing to the population size.

With a constant growth rate and centuries of time, populations can expand exponentially. The most comprehensive analysis of shipping records over the course of the slave trade is the Trans-Atlantic Slave Trade Database, edited by professors David Eltis and David Richardson, according to Henry Louis Gates Jr. in an article from 2014 in The Root.

Gates is a literary critic, professor, historian, and filmmaker who serves as the Alphonse Fletcher University Professor and the director of the Hutchins Center for African and African American Research at Harvard University. Since 2012, Gates has been the host of the television series “Finding Your Roots” on PBS.

And, according to the database, between 1525 and 1866, 12.5 million Africans were shipped to the New World. Some 10.7 million survived the horrific Middle Passage, disembarking in North America, the Caribbean and South America.  In North America, about 388,000 were brought ashore, USA Today reported.

While Gates noted there are 40 million African Americans, but The Moguldom Nation is using 35 million, excluding non-native Black Americans.

Given a constant rate of growth, a population will not just increase, but will do so at an accelerating rate, assuming that the growth conditions remain consistent.

Here’s a simplified breakdown:

1. Initial Population (P0): Less than 450,000 African slaves.
2. Growth Rate (r): This is not just the birth rate but the rate of population increase after accounting for deaths. Even a modest growth rate can lead to large increases over time.
3. Time (t): Several centuries (from the 17th century to the 21st century).
4. Compound Growth Formula: The general formula for population growth is P(t)=P0×ert, where P(t) is the future population, e is the base of the natural logarithm, and t is time.

With a constant growth rate and centuries of time, populations can expand exponentially.

Henry Louis Gates Jr., Photo via Twitter/X, https://twitter.com/HenryLouisGates/photo