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Thread: A simple formula to count percents?

  1. #1
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    A simple formula to count percents?

    I'm really bad in counting percents. Can you explain me a simple way to solve the following problem. I'd appreciate it a lot

    - The population of a city raised each year X times compared to the last year. This happened ten years (ten times) and in the end the population was twice as large as in the beginning.

    How will I find out what the X is ?
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by Liza88 View Post
    I'm really bad in counting percents. Can you explain me a simple way to solve the following problem. I'd appreciate it a lot

    - The population of a city raised each year X times compared to the last year. This happened ten years (ten times) and in the end the population was twice as large as in the beginning.

    How will I find out what the X is ?
    You must have heard of GP
    $\displaystyle
    A, Ar, Ar^2 , Ar^3......
    $
    nth term of GP( geometric progression)
    $\displaystyle Ar^{n-1}$ ... A is first term , r is the Common ratio

    Let initial population is P
    So 10 th year the population is

    $\displaystyle P*X^{10-1}$
    Hence

    $\displaystyle P*X^9= 2*P$

    $\displaystyle X^9 =2$

    $\displaystyle X=2^{\frac{1}{9}}$
    Last edited by ADARSH; Feb 4th 2009 at 01:32 AM.
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    Oops Just noticed you wanted percentage

    I am giving you a sample
    Percentage of any value x in a total quantity (x+y) is given by

    $\displaystyle
    Percentage=\frac{x * 100}{x+y}
    $

    .............................................
    For finding percentage increase after 10 years

    $\displaystyle
    \frac{\text {(Population after 10 years - Initial Population)}*100}{\text{Initial Population}}
    $
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