# Can you interpret this please?

Discussion in 'Mathematics' started by anon1021, Mar 20, 2012.

1. ### anon1021

I've been doing a little maths on exponents. When I plotted my results I expected to see a graph that developed exponentially but instead I ended up a long line across the x axis very close to 0 and then a straight line up to the last number. Please can tell me what I've done wrong/ how i've misinterpreted my results? (base number was 125)
Any help would be greatly appreciated.
Thanks
P
<table cellpadding="0" cellspacing="0" style="width:311pt;border-collapse:collapse;"><tr style="height:12.75pt;"><td style="background-color:transparent;width:59pt;height:12.75pt;border:#ece9d8;" align="right">1</td><td style="background-color:transparent;width:252pt;border:#ece9d8;" align="right">125</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">2</td><td style="background-color:transparent;border:#ece9d8;" align="right">15625</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">3</td><td style="background-color:transparent;border:#ece9d8;" align="right">1953125</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">4</td><td style="background-color:transparent;border:#ece9d8;" align="right">244140625</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">5</td><td style="background-color:transparent;border:#ece9d8;" align="right">30517578125</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">6</td><td style="background-color:transparent;border:#ece9d8;" align="right">3.8147E+12</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">7</td><td style="background-color:transparent;border:#ece9d8;" align="right">4.76837E+14</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">8</td><td style="background-color:transparent;border:#ece9d8;" align="right">5.96046E+16</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">9</td><td style="background-color:transparent;border:#ece9d8;" align="right">7.45058E+18</td></tr></table>

2. ### anon1021

I've been doing a little maths on exponents. When I plotted my results I expected to see a graph that developed exponentially but instead I ended up a long line across the x axis very close to 0 and then a straight line up to the last number. Please can tell me what I've done wrong/ how i've misinterpreted my results? (base number was 125)
Any help would be greatly appreciated.
Thanks
P
<table cellpadding="0" cellspacing="0" style="width:311pt;border-collapse:collapse;"><tr style="height:12.75pt;"><td style="background-color:transparent;width:59pt;height:12.75pt;border:#ece9d8;" align="right">1</td><td style="background-color:transparent;width:252pt;border:#ece9d8;" align="right">125</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">2</td><td style="background-color:transparent;border:#ece9d8;" align="right">15625</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">3</td><td style="background-color:transparent;border:#ece9d8;" align="right">1953125</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">4</td><td style="background-color:transparent;border:#ece9d8;" align="right">244140625</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">5</td><td style="background-color:transparent;border:#ece9d8;" align="right">30517578125</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">6</td><td style="background-color:transparent;border:#ece9d8;" align="right">3.8147E+12</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">7</td><td style="background-color:transparent;border:#ece9d8;" align="right">4.76837E+14</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">8</td><td style="background-color:transparent;border:#ece9d8;" align="right">5.96046E+16</td></tr><tr style="height:12.75pt;"><td style="background-color:transparent;height:12.75pt;border:#ece9d8;" align="right">9</td><td style="background-color:transparent;border:#ece9d8;" align="right">7.45058E+18</td></tr></table>

3. ### PaulDGOccasional commenter

Your numbers increase by a factor of 125 each time - the last number is 125 times as big as the one before it.

The curve is there, the problem is your piece of paper simply isn't big enough to show it on the scale you have.

(If you plotted the first number 1.25 centimetres from the axis, the last number in your series would need to be plotted somewhere near the opposite end of the galaxy!, so when you plot that last number on the same planet as all the others, those others are all going to be pretty close to each other...)

5. ### anon1021

Thank you both!

6. ### PaulDGOccasional commenter

Don't worry.

Try it again with a smaller base. "1.25" would be a good start. "2" is a good place to stop - once you get to "3", exponential growth already means the problem you've seen begins to be significant.

7. ### anon1021

I will do that now - thank you.

I'm actually trying to find out what the largest number would be using the numbers 0123456789. I have a feeling it's going to be exponential and that it will be to a significantly large power.
Does anyone know of another software programme that would enable me to explore these large numbers?
My logic seems to draw a blank when I hit larger numbers!
(I'm fighting between 9876^543210 and 543210^9876 and could really do with seeing the results)

Thanks
P

8. ### anon1021

Just tried the 1.25 base - gave me a v clear exponential graph - Thank you!

9. ### PaulDGOccasional commenter

Which is bigger: 543210log(9876) or 9876log(543210) ?

10. ### PaulDGOccasional commenter

PS 98^76 > 9876

and 543^210 > 543210

11. ### SC00BY

(2!^3!^4!^5!^6!^7!^8!^9!^10!)!
Not quite sure how big that would be but im guessing its pretty big!

12. ### GoldMathsNew commenter

I'm confused why there is no right answer??

Surely there are a finite amount of operations available to us as well as a finite combination of the 10 digits?

As I right this I have thought is my first assumption fair? Why cant you/we do (((((9)!)!)!)!)!) so guessing without some criteria we would be finding infinity.

13. ### anon1021

Because it totally depends on the parameters set.
Exactly!
I like this one!

14. ### D Franklin

This isn't right. In the absence of brackets, you should evaluate from right to left.

For example, 2^3^4 is equivalent to 2^(3^4).

So 2^3^4 = 2^81, which is much much bigger than 32^4.

The difference is even greater when considering 2^3^4^...^9.

You could use First Knuth&rsquo;s Up-Arrow Notation method of writing very large numbers...
3&uarr;&uarr;&uarr;3
for instance is on the cosmic scale...
but factorial does a similar, if somewhat less impressive, job.