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baddtude

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I'm not a math student or professor, so please bare with me. I have an unusual question. I am trying to figure out the mathimatical calculation to a table to recreate. As I said, I'm not a mathmetician. Here is what I'm trying to figure out. From these numbers: 78, 118, 178, 269, 406, 613, 925, I am trying to determine the equation that would make 78 become 118, 118 become 178, 178 become 269, and so on. I'm inclined to believe that the equation is a POWER formula. Like 78^0.509=118. That is true, but that formula doesn't maintain through out the series of numbers.
 


Hello baddtude:

When you wrote "to recreate", were you trying to say that mathematical recreation (i.e., fun) is your motivaion, or were you trying to say that you're creating this table anew? It really doesn't matter (to me); I just find ambiguities in contemporary English curious.

So, you wrote 78^0.509 = 118.

The exponent 0.509 is not correct.

78^0.509 = 9.18494 (rounded to five decimal places)

The correct exponent cannot be exactly written as a number because it's irrational. If we want to express this exponent exactly, then we need to use logarithms.

The exact exponent is the ratio ln(118)/ln(78). A decimal approximation is 1.09502 (to five places).

78^1.09502 = 117.99984

The more decimal places we use in the approximation, the closer the power becomes to 118.

78^1.095020304143352408329059876549 = 117.99999999999999999999999999992576541580962

Okay — enough of that!

The exponents required to raise each number in your sequence to obtain the subsequent number are all different, so exponentiation alone won't work. Here are the next three exponents (decimal approximations rounded to five places).

118^1.08617 = 177.998

178^1.07969 = 269.002

269^1.07358 = 406.007

Can you provide some more details regarding where you found this exercise? Is there any additional information given? What does the table look like?

At first glance, I don't recognize any set of elementary operations that, consistently applied to any number in the sequence, would generate the subsequent number. I like brain-teasers, but I'm going to wait to see if you post more details, before diving in any deeper.

Cheers,

~ Mark

 
Thank you for your reply, Mark. And, I apologize for any ambiguity I unintentially posted. If you're curious, I'm American (I noticed this site was global). 1st, let me say, this is not an excersize or a brain teaser. The table is part of a game. Those numbers I provided are the costs of a construct and subsequent upgrades. The table is limited in how high it goes, and in an attempt to expand it, I have been trying to figure out what the formula was so I may make a spreadsheet in Excel that could calculate the levels beyond the available information. I hope I haven't given the impression of a puzzle. For me it is, as I stated, I'm not a math scholar. I had hoped in providing those numbers, someone would see something I'm not. But, I can see from your example, I left out an important detail.

118^1.08617 = 177.998

178^1.07969 = 269.002

269^1.07358 = 406.007

1 thing that makes the differnce is the numbers I provided are undoubtedly rounded, but not necessarily up or down. My apologies again. The formula is good as long as it rounds to the whole number, even though the exponent is not a round number.

Of course, I state again, I'm inclined to think it was an equation with a POWER formula. I could be wrong. My inclination is derived from other equations in the game that I have been provided a formula for, all have been a Power formula. I was simply assuming that could be a common trend. It has been a long time since I took a math course, and have forgotten how to use a scientific calculator, although, I haven't ever been taught how to use for anything except statistics. So, I thought I would search the internet for something that might help determine the formula. Unfortunately, once you get beyond algebra, I start to become disoriented and am unfamiliar with the meaning of most calculus, trigonometry and other advanced math terms and jargon.

Again, thank you for your response.
 


Hey, no need to apologize for anything. The English language is inherently ambiguous. I'm not curious about your citizenship; I was interested in knowing whether or not I was reading an example of somebody using the phrase "to recreate" to mean "for the purposes of recreation" (i.e., fun).

(By the way, the statement that you're "American" is also ambiguous. Are you from Canada? Brazil? Jamaica? Mexico? Or one of the other countries in the Americas? If you were to state, instead, that you're North American, then that would narrow it down to two possibilities!)

I would like to know about this game, that you're not playing for recreation.

Can you show me some of the prior numbers and equations that you referenced?

~ Mark

 
Re:

mmm4444bot said:


(By the way, the statement that you're "American" is also ambiguous. Are you from Canada? Brazil? Jamaica? Mexico? Or one of the other countries in the Americas? If you were to state, instead, that you're North American, then that would narrow it down to two possibilities!)

Only!! - I thought NAFTA had three parties......

~ Mark

[/color]
Click to expand...
 
baddtude said:
I'm not a math student or professor, so please bare with me. I have an unusual question. I am trying to figure out the mathimatical calculation to a table to recreate. As I said, I'm not a mathmetician. Here is what I'm trying to figure out. From these numbers: 78, 118, 178, 269, 406, 613, 925, I am trying to determine the equation that would make 78 become 118, 118 become 178, 178 become 269, and so on. I'm inclined to believe that the equation is a POWER formula. Like 78^0.509=118. That is true, but that formula doesn't maintain through out the series of numbers.
Click to expand...

It is possible to write a function such that (78,118), (118,178), (178,269), (269,406), (406,613), (613,925) - but there is no guarantee that next number will follow the same rule of transformation.

This is a linear function where y = 0.24222 + 1.5088 * x
 
I guess to make things simpler, I'll just provide all information. The game I'm playing (yes, for recreation), is called Spaceinvasion. It is an internet browser game, (I believe) thats developed and supported by Bigpoint. The numbers I provided are part of the construction costs of a mining unit. The extent of information I have on the list of numbers is:
Level Construction Cost
1 78
2 118
3 178
4 269
5 406
6 613
7 925
8 1,397
9 2,109
10 3,184
11 4,807
12 7,259
13 10,961
14 16,550
15 24,991
16 37,736
17 56,981
18 86,041
19 129,922
20 196,181
My intent is to expand the table by use of a spreadsheet. From a fansite, other formulas were provided for other parts in the game, are POWER calculations. For instance:
Round (level^2)/2-1
When given that plainly, It's easy to create a table.

Anyway, thank you all for your responses.
BTW, further clarification, I'm from the United States.
 
Subhotosh Khan said:


… I thought NAFTA had three parties …
Click to expand...


Yeah, I know.

This is the sort of thing that happens, when politicians get involved. (Like Congress deciding that a tomato is legally a vegetable, or trying to set the value of Pi to 3.)

I prefer to align myself with educated people. :wink:

 
I generated an exponential equation of \(\displaystyle y=51.719559\cdot 1.509891^{x}\)

The Power regression was not too accurate.

Of course, the higher the x value, the further it strays. i.e if x=1, then y=78.09 and if x=20, then y=196140.257739.

This is probably about as accurate a model as can be expected.
 
galactus said:
I generated an exponential equation of \(\displaystyle y=51.719559\cdot 1.509891^{x}\)

The Power regression was not too accurate.

Of course, the higher the x value, the further it strays. i.e if x=1, then y=78.09 and if x=20, then y=196140.257739.

That's ~ 0.02% error - good enough for government work (as bigGlen would proclaim)

This is probably about as accurate a model as can be expected.
Click to expand...
 
baddtude said:
… determine the equation that would make 78 become 118, 118 become 178, 178 become 269, and so on …
Click to expand...


And to think that I had been considering a recursive formula. :roll:

 
baddtude said:
I guess to make things simpler, I'll just provide all information. The game I'm playing (yes, for recreation), is called Spaceinvasion. It is an internet browser game, (I believe) thats developed and supported by Bigpoint. The numbers I provided are part of the construction costs of a mining unit. The extent of information I have on the list of numbers is:
Level Construction Cost
1 78
2 118
3 178
4 269
5 406
6 613
7 925
8 1,397
9 2,109
10 3,184
11 4,807
12 7,259
13 10,961
14 16,550
15 24,991
16 37,736
17 56,981
18 86,041
19 129,922
20 196,181
My intent is to expand the table by use of a spreadsheet. From a fansite, other formulas were provided for other parts in the game, are POWER calculations. For instance:
Round (level^2)/2-1
When given that plainly, It's easy to create a table.

Anyway, thank you all for your responses.
BTW, further clarification, I'm from the United States.
Click to expand...

cost = ceil(78 * 1.51[sup:2ueaxwbt](level-1)[/sup:2ueaxwbt] )

From, a non-north-American... ;-)
 
DrMike said:
cost = ceil(78 * 1.51[sup:15moqb6s](level-1)[/sup:15moqb6s] )

From, a non-north-American... ;-)
Click to expand...


Please excuse my ingorance, but what is 'ceil'? As I stated earlier, I'm not a student of math. This would be 1 of those terms (jargon) that I'm not familiar with.

Sorry about this question. A searchengine search on the term "ceil" gave me the information I needed quite quickly. I entered this into my spreadsheet, and it matches what information I have available without error. Thank you very much.
 
Ceiling is a function such that it is the smallest integer not less than x.

For instance, 3.8. The ceiling would be 4. As opposed to the floor function. The floor of 3.8 would be 3.
 
baddtude said:
DrMike said:
cost = ceil(78 * 1.51[sup:1bj43gr5](level-1)[/sup:1bj43gr5] )

From, a non-north-American... ;-)
Click to expand...


Please excuse my ingorance, but what is 'ceil'? As I stated earlier, I'm not a student of math. This would be 1 of those terms (jargon) that I'm not familiar with.

Sorry about this question. A searchengine search on the term "ceil" gave me the information I needed quite quickly. I entered this into my spreadsheet, and it matches what information I have available without error. Thank you very much.
Click to expand...

You're welcome.. :)
 
So, may I ask, how did you discover the formula? For further reference, it could come in handy to know how to do this.
 


Try a Google search on keywords: exponential regression best-fit curve

We generally use software to crunch the numbers (i.e., run the algorithm) to fit data to a trend.

The exponential function: y = a*b^x.

Basically, we take known (x, y) pairs, like (1, 78) (2, 118) (3, 178) (4, 269), and put this data through the steps in a regression algorithm, and we wind up with values for a and b, like a=78 and b=1.51. The numbers a and b act as parameters; we can change their values to bend the shape of the exponential curve such that the error between the curve and the actual data points is reduced as much as possible.

I learned the algorithm about 15 years ago, and then soon forgot it, after employing machines to do the work.

 
I feel a little stupid.
I have tried several search engines, and any online tools (calculators) do not give me the answer I was provided by DrMike.
DrMike said:
cost = ceil(78 * 1.51[sup:3c5svgiw](level-1)[/sup:3c5svgiw] )
Click to expand...

I guess I'm further removed from the math than I realized. So it seems, I am simply unable to do this without some assistance.
 
mmm4444bot said:
What tools did you try?
'[/color]
… I am simply unable to do this …
Click to expand...


When you write "this", do you mean "exponential regression"?
Click to expand...

Yes, 'this' is reference to exponential regression. Even with these online tools, I'm unable to produce an answer, even when I already know the answer. There are a couple more tables of numbers I want to generate a correct formula for.

Here's 1 Site I tried. Although I was able to get the numbers to be very close, it doesn't show the "-1" expressed in DrMike's equation, that is what truly makes the difference. It also seemed the most functional, but, I don't really understand what the 'Correlation Coefficient' is in this application.

http://www.zweigmedia.com/4eSite/newgra ... rames.html

This next site, seems like it has potential. I think it is my lack of understanding about the exponential regression that makes this hard for me to work,

http://www.xuru.org/rt/ExpR.asp

Again, my biggest obsticle seems to be that I get lost in what I'm actually reading in the far too simple explanations. I've come to the conclusion that I will have to do a bit of reading so I can completely comprehend how exponential regression works (I suspect it will also require a little reading of matertial that create the foundations of this particuliar math).
 
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