SOLUTION: The population of an island increases by 10% each year. After how many years will the original population be doubled?

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Question 800321: The population of an island increases by 10% each year. After how many years will the original population be doubled?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +P+ = the starting population
Let +p+ = the population for the current year
Start of 1st year:
+p+=+P+
----------
Start of 2nd year:
+p+=+P+%2B+.1P+
---------------
Start of 2nd year:
+p+=+P+%2B+.1P+%2B+.1%2A%28+P+%2B+.1P+%29+
+p+=+%28+P+%2B+.1P+%29%2A%28+1+%2B+.1+%29+
+p+=+P%2A%28+1+%2B+.1+%29%5E2+
---------------
Start of 3rd year:
+p+=+P%2A%28+1+%2B+.1+%29%5E3+
---------------
In what year +n+ will +p+=+2P+?
+2P+=+P%2A1.1%5En+
+2+=+1.1%5En+
+n%2Alog%281.1%29+=+log%282%29+
+n+=+log%282%29+%2F+log%281.1%29+
+n+=+.301+%2F+.0414+
+n+=+7.271+
After 7 years the population is doubled
check:
+2+=+1.1%5En+
+2+=+1.1%5E7.271+
+2+=+1.9997+
close enough