document.write( "Question 1160871: it is estimated that the population of a village increases by 10 percent every five years. if the population of the village is 150,000 this year, what will be the estimated population ten years from now? \n" ); document.write( "
Algebra.Com's Answer #784274 by Theo(13342)\"\" \"About 
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the population increases by 10% evey five yhears.
\n" ); document.write( "f = p * (1 + r) ^ n
\n" ); document.write( "f is the future value
\n" ); document.write( "p is the presnt value
\n" ); document.write( "r is the interest rate per time period
\n" ); document.write( "n is the number of time periods.
\n" ); document.write( "the time periods are every 5 years.
\n" ); document.write( "the formula becomes:
\n" ); document.write( "f = 150,000 * (1 + .10) ^ 2
\n" ); document.write( "solve for f to get:
\n" ); document.write( "f = 181,500.
\n" ); document.write( "that's your solution.
\n" ); document.write( "in 10 years, there are 2 five year periods, therefore n = 2.
\n" ); document.write( "if you wanted to solve for the annual growth rate in this problem, you would do the following.
\n" ); document.write( "p = 1
\n" ); document.write( "f = 1.10
\n" ); document.write( "r = (1 + r)
\n" ); document.write( "n = 5
\n" ); document.write( "formula becomes:
\n" ); document.write( "1.1 = 1 * (1 + r) ^ 5
\n" ); document.write( "this becomes 1.1 = (1 + r) ^ 5
\n" ); document.write( "take the fifth root of both sides of this equation to get:
\n" ); document.write( "1.1 ^ (1/5) = 1 + r
\n" ); document.write( "subtract 1 from both sides of this equaation to0 get:
\n" ); document.write( "1.1 ^ (1/5) - 1 = r
\n" ); document.write( "solve for r to get:
\n" ); document.write( "r = .0192448765.
\n" ); document.write( "that's the annual growth rate.
\n" ); document.write( "with your time periods in years, rather than every 5 years, f = 150,000 * (1 + .0192448765) ^ 10 gets you:
\n" ); document.write( "f = 181,500.
\n" ); document.write( "same answer, as it should be if you did everything correctly.\r
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