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What is exponential growth?

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University Course Reader · STEM

Under exponential growth, the population doubles every generation regardless of how large it has already become.

The reader highlighted one word in a textbook passage. Clicked broke down the concept “exponential growth” into plain English:

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Overview

Exponential growth is growth that multiplies rather than adds. What gets added each round depends on how big the thing already is. Take 100 growing at 10% a year: the first year adds 10, and the tenth year adds nearly 24. The rate never changed. Only the number it was applied to did.
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Overview

Exponential growth means the thing multiplies each round instead of picking up a set lump. What it adds is worked out from its current size, so the jumps keep swelling even when the rate has not budged. Round one feels like a waste of time. Round nine feels like an explosion. Same rule running both times. 😎

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Detail

Start with 100 rabbits and let the population rise 20% a year. Year one adds 20. Year two adds 24. Year five adds nearly 42. By year twenty, a single year adds more rabbits than existed at the start, which catches most people by surprise. Nothing about the rabbits changed, because the 20% held steady the whole time. Why not just call it fast growth? Because fast usually means a fixed amount each year, like a factory adding 500 units, and multiplying overtakes adding sooner or later every time. The trouble is that the early years look like nothing is happening. Plans get made on the strength of that flat start, and those plans fall apart when the big numbers arrive on schedule. It turns up in compound interest, epidemics and viral posts, and running backwards it is what a half-life describes.
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Detail

A post gets 10 shares. Each of those brings 10 more. By round five you are looking at 100,000. Nobody improved the post along the way, every round just started from a bigger crowd than the last one. So why not label it fast growth and move on? Because fast usually means a steady lump, like a shop pulling in 50 new customers a month, and the multiplying kind wins that race sooner or later without fail. The rough part is that the opening rounds look like total failure, so people bail at round three and miss the bit they were waiting for. Outbreaks and savings accounts are the same shape but running at wildly different speeds, which is why one takes a fortnight and the other takes thirty years. 😎

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Analogy

A savings account paying 5% is the everyday version. Put in 1,000 and the first year pays 50, which is unexciting. The tenth year pays about 78, without the rate ever moving. Leave it forty years and a single year pays more than six times what the first year did. Every year starts from a bigger balance than the last, which is the entire idea.
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Analogy

Fold a piece of paper. One fold gives two layers. Ten folds give about a thousand. Forty-two folds would in theory reach the moon, which sounds like a lie invented to sell calculators until you check the arithmetic. Every fold only doubles what you already had. The first few look pointless and the last few sound impossible, and both are the same doubling. 😎
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AI explanations may contain errors · Not professional advice

Formal definition — The same term, explained the usual way

Exponential growth occurs when the rate of increase of a quantity is proportional to its current value, producing a constant multiplicative factor per unit time rather than a constant additive increment. Any exponential process with a positive rate eventually exceeds any linear process, irrespective of their relative starting values, and plots as a straight line on a logarithmic axis.

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