If the population of a town doubles every 10 years

the population in the year X +100 will be how many times the population in year X?
Please answer ASAP i have my SATs tommorow!

in 100 years, at 10 years per doubling, there will be 10 doublings.

2x2x...x2 = 2^10 = 1024

Where "p" is the initial population "c" is the current population and "x" is the number of years since the initial year; your basic equation for the population in a given year is: c = p * 2 ^ ((x-1)/10). So "c" the current pop. will double every 10 years.

now, how many times bigger the population is after 100 years: add 100 to x and divide it your new formula by the original formula:

(p*2^((100+x-1)/10))/(p*2^((x-1)/10))

cancel the "p's" and simplify

2^((x+99)/10)/2^((x-1)/10)

now pick ANY number and plug it in to x. no really ANY number. we'll go with 42.

2^((42+99)/10)/2^((42-1)/10)

2^14.1/2^4.1

17559.936/17.148375

1024

so the pop. in year x+100 will be 1024 times the pop. in year x.

I used 42 to illustrate that it will work with ANY number not just 1, 11, 21...

I presented this more as a proof then an easy to use method if you're going into a standardized test with limited time to answer each question you go with a more simplified solution (ie: ten doublings mean 2x2x2x2x2x2x2x2x2x2=1024 times bigger)