document.write( "Question 1159780: A firm decided to increase its output from its current level of 60,000 to 70,000. Assume that the
\n" ); document.write( "compounded interest required to achieve this growth is 10%. Find the number of years needed to
\n" ); document.write( "reach the required output. \n" ); document.write( "
Algebra.Com's Answer #782948 by Theo(13342)\"\" \"About 
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compound interest formjla is f = p * (1 + r) ^ n
\n" ); document.write( "f is the future value
\n" ); document.write( "p is the present 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( "in your problem:
\n" ); document.write( "p = 60,000
\n" ); document.write( "f = 70,000
\n" ); document.write( "r = 10% per year.
\n" ); document.write( "n = number of years.
\n" ); document.write( "formula becomes 70,000 = 60,000 * (1 + .10) ^ n
\n" ); document.write( "divide both sides of this equation by 60,000 to get:
\n" ); document.write( "70,000 / 60,000 = (1 + .10) ^ n
\n" ); document.write( "simplify to get:
\n" ); document.write( "7/6 = 1.1 ^ n
\n" ); document.write( "take the log of both sides of this equation to get:
\n" ); document.write( "log(7/6) = log(1.1^n)
\n" ); document.write( "since log(1.1^n) = n * log(1.1), the equation becomes:
\n" ); document.write( "log(7/6) = n * log(1.1)
\n" ); document.write( "solve for n to get:
\n" ); document.write( "n = log(7/6) / log(1.1) = 1.617357979 years
\n" ); document.write( "60,0000 output will increase to 70,000 output in that many years.
\n" ); document.write( "confirm by replacing n in the original formula with that to get:
\n" ); document.write( "f = 60,000 * 1.1 ^ 1.617357979 = 70,000.
\n" ); document.write( "this confirms the solution is correct, assuming the correct formula was used. \n" ); document.write( "
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