In the last post, he mentioned derivatives, which is calculus. He's doing it the hard way.
The "exponential function" is e = 2.72.... , an unending number like pi. You've probably seen e before. Lots of science depends on raising e to a power. It's just something you see again and again. That's how I got familiar with it.
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12162008, 01:35 PM #41You can't spell "justice" without ISTJ.

12162008, 01:37 PM #42
Henri Poincare noted a difference between those who fared better in algebra and those who did well in geometry. He said that those in geometry used something of a guessandcheck method with intuition, narrowing down the possibilities toward a direct answer. To the contrary, those who do well in algebra seek to prove something straight forward and directly, getting to the point immediately and in a linear fashion.
I did better in algebra in high school, though I'm not absolutely sure which one would be my best. Probably algebra.
I would also posit that those studies based on algebra are more abstract while the geometrical depend on more concrete faculties.

12162008, 01:37 PM #43
The derivative is taught in any introductory calculus course. Calculus is sometimes taught in grade 12. Other times people wait until college to take it. Exponential functions y=(constant)^x are taught in grade 12 algebra. While you can solve the problem without calculus just by recognizing that when the constant is less than 1 it is decreasing and greater than 1 it is increasing, it is less rigorous and involves memorization of specific cases of specific functions (easy to forget after the exam is over).

12162008, 01:39 PM #44

12162008, 01:45 PM #45
I had a really cool professor freshman year who explained how e was connected to the process of "taking something to a power", and when you think about it, that's why they call it an exponential function. At least, that's what I got from it.
You can't spell "justice" without ISTJ.

12162008, 02:06 PM #46
e=(1+1/n)^n as n goes to infinity.
It's an irrational number, just like pi.
If you want to see what it looks like to more decimal places check this out.
e is commonly used in this (y=e^x) form because it gains a lot of valuable properties.
The most important one is that it's easy to calculate its derivative.

12162008, 07:45 PM #47
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