Exponential Growth · Interactive

The Petri Dish Problem

A dish that doubles every minute looks nearly empty right up until the moment it isn’t. Guess when it’s half full, then watch doubling do the thing our intuition never sees coming.

Watch the Dish Fill

Bacteria double every minute; the dish is full at minute 60. Drag to any minute, or lock a guess for “half full” and press Play. Keep an eye on how empty it looks for how long.

3%
of the dish covered — minute 55

 

Exponential vs. The Wall

Real colonies can’t double forever — they run out of food and room. Watch unchecked doubling (which races off the top) against realistic growth that bends into an S and stalls at its ceiling. The dot marks where growth is fastest.

 

Fraction covered at minute t is 2^(t−60): half at minute 59, a quarter at 58, and only about 3% at minute 55. Realistic growth follows the logistic curve, whose steepest climb sits exactly at half the carrying capacity.

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