The rice and chessboard problem: why exponential growth fools your brain
Doubling time: the exponential growth hidden in compound interest and outbreaks
Money that grows by 7% a year doubles in about 10 years, even though 7% sounds small. The same quiet doubling hides in a credit card debt and in the first weeks of an outbreak. Learn to spot exponential growth when nobody says the word "double", and a quick trick to time it.
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1
Miva gives Rono a happier case first. Say he has $1,000 of savings, and they grow by 7% a year. Seven percent sounds small, and nobody says the word "double".
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2
In year 1, the money grows by $70. In year 2, the 7% is counted on $1,070, so it grows by $75. Interest earned on interest is called compound interest. Each year, the growth gets a little bigger.
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3
Keep going, and the $1,000 becomes about $2,000 in 10 years, then about $4,000 in 20 years. The same percent every year is doubling in disguise. A quick trick gives the doubling time: divide 70 by the percent. 70 divided by 7 is 10 years.
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4
Rono's credit card bill works the same way, but against him. Say he owes $1,000 at 24% a year and pays nothing back. 70 divided by 24 is about 3, so the debt doubles in about 3 years.
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5
Just then, the radio on the shelf gives the news. A new illness has appeared far away, with 100 cases. At the start of an outbreak, cases can double every few days. At one doubling every 3 days, 100 cases become about 100,000 in a month.
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6
A pond, savings, a debt and an outbreak. Each one grows by the same share at every step, so each one doubles at its own steady pace. And none of them has stopped yet.
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Quick check
A town that grows a little every year.
Show the answer
About 35 years. The same percent every year is doubling, and 70 divided by 2 is 35.
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Go further
The name of the trick, and a real outbreak.