I just thought I’d let everyone know that the Crash Course has inspired me in more ways than one. Last week I had an interview for a PGCE in Maths (Teacher training) and had to think of a maths problem to present as if to a class of year 9 kids, This is what I came up with. They must have liked it cos they offered me a place on the course:

The Exponential Eye-Dropper

And the Power of Compound Interest

Suppose I had a magic eye dropper and I placed a single drop of water, 1mm3, in the middle of your left hand. The magic part is that this drop of water is going to double in size every minute.

At first nothing seems to be happening, but by the end of a minute, that tiny drop is now the size of two tiny drops and it continues to double in size every minute.

To make this really interesting lets suppose that the classroom is watertight.

**Question 1:** My question to you is, “How long do we have to escape the classroom?”

When would it be completely filled? In hours? days? weeks? months? How long would that take?

**Question 2:** At what time is the classroom still 95% empty space?

**Question 3:** With this magic eyedropper what is the rate of growth?

**Question 4:** What is this kind of growth called?

**Question 5:** If we were to plot the change in water volume over time on a chart what would it look like?

**Question 6:** Can we think of anything else that grows by a certain percentage all the time?

Bacteria show a classic example of exponential growth, and similar patterns can be found all through nature. The growth is exponential for as long as food, oxygen, etc. are in sufficient excess to not physically limit growth.

If nutrients can be supplied at a constant rate, population stabilizes at a certain level (e.g. activated sludge plant receiving steady wastewater flow) in the endogenous or death phase. But if it’s a closed system with no new supply, look out!

Tom

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I’d be interested in hearing the answers as a room may be more relate-able.

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Hi there,

Well interestingly, and maybe this will show you the power of exponential growth even clearer. If I said it takes the average classroom about 30-35 minutes to fill, compare that with Fenway park which takes 49 minutes to fill. not much difference in the time to fill, but vastly different capacities. It goes from filling a classroom to filling Fenway park in just 14 minutes.

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