document.write( "Question 1129963: Use the average growth rate between 1850 and​ 1950, which was about 0.7%, to find the approximate doubling time and to predict the population in 2050 of a growing suburban town​ (based on a 2000 population of​ 100,000). Round to the nearest year and person.\r
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\n" ); document.write( "B.100 ​years; 2050 population=141,421
\n" ); document.write( "C.95 ​years; 2050 population=123,114
\n" ); document.write( "D.110 years; 2050 population=131,951
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Algebra.Com's Answer #746589 by Theo(13342)\"\" \"About 
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the average growth rate between 1850 and 1950 is equal to .7% which is equal to .007.\r
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\n" ); document.write( "\n" ); document.write( "the formula to use is f = p * (1 + r) ^ n\r
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\n" ); document.write( "\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\r
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\n" ); document.write( "\n" ); document.write( "if the 2000 population is 100,000, then doubling it will result in 200,000.\r
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\n" ); document.write( "\n" ); document.write( "the formula becomes 200,000 = 100,000 * (1 + .007) ^ n\r
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\n" ); document.write( "\n" ); document.write( "divide both sides of the equation by 100,000 and simplify to get:\r
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\n" ); document.write( "\n" ); document.write( "2 = 1.007 ^ n\r
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\n" ); document.write( "\n" ); document.write( "take the log of both sides of the equation to get:\r
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\n" ); document.write( "\n" ); document.write( "log(2) = log(1.007 ^ n) which is the same as log(2) = n * log(1.007).\r
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\n" ); document.write( "\n" ); document.write( "solve for n to get:\r
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\n" ); document.write( "\n" ); document.write( "n = log(2) /log(1.007) = 99.36719646, which is closer to 100 than any of the other selections.\r
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\n" ); document.write( "\n" ); document.write( "note that rule of 70 would have gotten you 70 / .7 = 100.\r
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\n" ); document.write( "\n" ); document.write( "at .7% annual interest rate for 50 years, the formula becomes:\r
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\n" ); document.write( "\n" ); document.write( "f = 100,000 * (1.007) ^ 50.\r
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\n" ); document.write( "\n" ); document.write( "this results in f = 141,734.\r
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\n" ); document.write( "\n" ); document.write( "this is closer to 141,421 than any of the other selections.\r
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\n" ); document.write( "\n" ); document.write( "your solution points to selection B.\r
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