CM’s CC inspires new Maths Teacher
Hi there,
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 EyeDropper
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?

Fri, Feb 05, 2010  12:57am
#2Peak Prosperity Admin
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I’d be interested in hearing the answers as a room may be more relateable.

Fri, Feb 05, 2010  03:09am
#3Peak Prosperity Admin
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The room is a size that’s a bit easier to grasp.
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

Fri, Feb 05, 2010  03:12am
#4Peak Prosperity Admin
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I just finished sending instructions on how to make yogurt to a young friend, when I jumped over here and read this. This is yogurt too isn’t it? The best time to eat it is the stationary phase.

Fri, Feb 05, 2010  02:11pm
#5Peak Prosperity Admin
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[quote=Davos]
I’d be interested in hearing the answers as a room may be more relateable.
[/quote]
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 3035 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.
Thu, Feb 04, 2010  09:24pm
#1CM’s CC inspires new Maths Teacher