# Thread: A simple formula to count percents?

1. ## 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 ?

2. Originally Posted by Liza88
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

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

$\displaystyle X^9 =2$

$\displaystyle X=2^{\frac{1}{9}}$

3. 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

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