# The population of an island increases by 10% each year.  After how many years will the original population be doubled? Let the original population of the island be P. Now the population is increasing at 10% every year. But we have to remember that we have to use the formula for compounding here as those who are born also increase in number by 10% the next year.

So we have...

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Let the original population of the island be P. Now the population is increasing at 10% every year. But we have to remember that we have to use the formula for compounding here as those who are born also increase in number by 10% the next year.

So we have P*(1+r)^n = 2P , where r = 10% = 0.1 and N is the number of years required.

=> P*1.1^n = 2P

=> 1.1^n = 2

this can be easily solved using logarithms.

n log 1.1 = log 2

=> n = log 2/ log 1.1

=> n = 7.2725

So the population of the island doubles in 7.2725 years.

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