Humans are the most populous large mammal on Earth today, and probably in all of geological history. This World Population Day, humans number in the vicinity of 7.5 to 7.6 billion individuals.

Can the Earth support this many people indefinitely? What will happen if we do nothing to manage future population growth and total resource use? These complex questions are ecological, political, ethical – and urgent. Simple mathematics shows why, shedding light on our species’ ecological footprint.

The mathematics of population growth

In an environment with unlimited natural resources, population size grows exponentially. One characteristic feature of exponential growth is the time a population takes to double in size.

Exponential growth tends to start slowly, sneaking up before ballooning in just a few doublings.

To illustrate, suppose Jeff Bezos agreed to give you one penny on Jan. 1, 2019, two pennies on Feb. 1, four on March 1, and so forth, with the payment doubling each month. How long would his $100 billion fortune uphold the contract? Take a moment to ponder and guess.

After one year, or 12 payments, your total contract receipts come to US$40.95, equivalent to a night at the movies. After two years, $167,772.15 – substantial, but paltry to a billionaire. After three years, $687,194,767.35, or about one week of Bezos’ 2017 income.

The 43rd payment, on July 1, 2022, just short of $88 billion and equal to all the preceding payments together (plus one penny), breaks the bank.

Real population growth

For real populations, doubling time is not constant. Humans reached 1 billion around 1800, a doubling time of about 300 years; 2 billion in 1927, a doubling time of 127 years; and 4 billion in 1974, a doubling time of 47 years.

On the other hand, world numbers are projected to reach 8 billion around 2023, a doubling time of 49 years, and barring the unforeseen, expected to level off around 10 to 12 billion by 2100.

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