You are not logged in.
#1 2005-09-18 02:33:08
- Sten
- Novice
Offline
Working backwards from a formula
I've always been terrible at working backwards from a formula.
units = 300 * (growingNumber^1.1)
The above formula determines how many units a certain item requires to complete. Each additional item increases in unit consumption to complete. My task is to determine a formula that will return the total number of items that can be built, given a certain number of units.
ie.
The above formula produces:
Item# Units
1 300
2 643
3 1,005
4 1,378
5 1,762
6 2,153
7 2,551
8 2,955
9 3,363
10 3,777
If a person has 5008 units, he can then produce 5 total Items (300+643+1005+1378+1762 = 5008).
How can I create a formula to determine that 5 total items can be produced with 5008 units, without actually calculating up every unit cost per item?
Any help would be greatly appreciated.
Regards,
Sten
#2 2005-09-18 08:17:17
- MathsIsFun
- Administrator
Online
Re: Working backwards from a formula
Hmmm ... without the power of 1.1 it is fairly easy to calculate the "cumulative sum" - it is the average times the count.
For example, the cumulative sum of 1,2,3,4,5 is the average value (3) times the count (5) = 3x5 = 15, and the average of a series of numbers can be worked out by just averaging the first and last (ie (1+5)/2 = 3)
But the " ^1.1 " makes it a geometric series, not linear ...
So I think we are looking at "Power Sums", a slightly tricky area of mathematics that I don't have enough knowledge of.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman