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An example need to be turned into an integral

  1. Nov 19, 2014 #1
    OK. We are producing something and then storing it. The first year, "1" is produced, the second year, "1,1" the third 1,12, so that the production capacity increases 10% per year. How do we convert this into a general formula for how much we have produced in total after year x?

    It is obviously an integral, but all formulas I find for ∫ nx give nonsense when I apply them to this example, so I think I'm wrong in turing the formula into nx

    How do I solve this?
     
  2. jcsd
  3. Nov 19, 2014 #2

    Mentallic

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    What you're looking for is called a geometric sum.

    [tex]S=1+r+r^2+...+r^{n-1}=\frac{r^n-1}{r-1}[/tex]

    r is the ratio, in your case 1.1, n is the amount of years you're counting.
     
  4. Nov 19, 2014 #3
    Ah, that gives reasonable numbers. So the formula resulting from the example is discrete? Is it the non-integer factor (1,1) that does that?

    EDIT: No, I specified the increase as happening annually, if it isn't, if it is continous, the (r-1) is replaced with ln(r), which I found by experimenting, and it gives exactly the value my calculator does. Oddly I cannot seem to find any reference to this formula, though I'm most cenrtainly again screwing up annotations.

    I need to refreshen my math-math, I've been in the world of molecules for too long...
     
    Last edited: Nov 19, 2014
  5. Nov 19, 2014 #4

    SteamKing

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    If the increase in production was constantly changing, every minute of every day saw an incremental increase, then you might use an integral to find the increase after a certain period. The integral is the limit of a certain process which can often be crudely represented as a summation.
     
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