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With the function f(x)=x^2 we get a graph like so...

x^2

The rule for power functions, that I've been told, is the larger the power gets, the closer the line will touch the x-axis.

Example for f(x)=x^10

x^10

My understanding the reason this is, is because no matter how many times you multiply 1/-1 you will always get 1 for the output. So you should always have the parabola curving vertically right at -1/1. That part makes complete sense.

My question is, when you multiply 0.9^200 it equals 7.05...

So, the input 0.9 and output 7.05.. do not seem to stay within the parabola because the parabola doesn't start going vertical till it hits -1/1 on the x-axis..

Am I seeing this right?

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$0.9^{200}\not=7.05$ Rather, $0.9^{200} = 7.05\times10^{-10}$ –  anorton Nov 5 '12 at 23:53
    
See here: .9^200 –  amWhy Nov 5 '12 at 23:55
    
@anorton so 7.05 x 10^-10 is not greater than 1? I don't understand how to read 10^-10 –  Tyler Zika Nov 5 '12 at 23:55
    
10^(-10) = 0.00000000001 –  anorton Nov 5 '12 at 23:57
    
@anorton Ah ha! That makes complete sense.. Thank you –  Tyler Zika Nov 5 '12 at 23:59
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2 Answers

Ok. The reason the graph of $y=x^n$ (where $n$ is an even integer) starts to "hug" the x axis for a greater distance as $n$ increases is that multiplying two numbers less than one returns a smaller value.

Essentially: $$x^n < x$$ if $x < 1, n >= 1$

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up vote 0 down vote accepted

My mistake. 0.9^200 does not equal 7.05. From the calculator, it says 7.05.. x 10^-10. The 10^-10 represents places in the tenths, hundredths, etc. So 0.9^200 does not equal 7.05... but in fact some ridiculously long decimal number in a "-ths" place I can't find a name for.

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In case anyone wants to know... it is the ten-billion-ths place, if I counted correctly. :) –  anorton Nov 6 '12 at 0:40
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@anorton you're awesome –  Tyler Zika Nov 6 '12 at 1:04
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