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.
The above formula produces:
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.
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