document.write( "Question 1206904: The population of Canada is 30 million people and is growing at an annual rate of 1.4%. The population of Germany is 80 million people and is decreasing at an annual rate of 1.7%. In how many years will the population of Canada be equal to the population of Germany?\r
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Algebra.Com's Answer #844631 by ikleyn(52800)\"\" \"About 
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\n" ); document.write( "The population of Canada is 30 million people and is growing at an annual rate of 1.4%.
\n" ); document.write( "The population of Germany is 80 million people and is decreasing at an annual rate of 1.7%.
\n" ); document.write( "In how many years will the population of Canada be equal to the population of Germany?
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document.write( "For the Canada population, the formula is\r\n" );
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document.write( "    C(t) = \"30%2A1.014%5Et\",  in millions.\r\n" );
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document.write( "For the Gremany population, the formula is\r\n" );
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document.write( "    G(t) = \"80%2A0.983%5Et\",  in millions.\r\n" );
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document.write( "t is the time in years from now.\r\n" );
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document.write( "The populatins are equal when  V(t) = G(t),  or\r\n" );
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document.write( "    \"30%2A1.014%5Et\" = \"80%2A0.983%5Et\".\r\n" );
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document.write( "It implies\r\n" );
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document.write( "    \"30%2F80\" = \"%280.983%2F1.014%29%5Et\",\r\n" );
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document.write( "or\r\n" );
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document.write( "    0.375 = \"0.969428008%5Et\".\r\n" );
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document.write( "Take log base 10 of both sides\r\n" );
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document.write( "    log(0.375) = t*log(0.969428008),\r\n" );
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document.write( "    t = \"log%28%280.375%29%29%2Flog%28%280.969428008%29%29\" = use your calculator = 31.58965618\r\n" );
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document.write( "Round to the closest integer to get the \r\n" );
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document.write( "ANSWER.  Approximately in 32 years.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other solved problems on exponential growth/decay,  look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Population growth problems \r
\n" ); document.write( "\n" ); document.write( "    - Radioactive decay problems \r
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\n" ); document.write( "\n" ); document.write( "    - Problems on appreciated/depreciated values \r
\n" ); document.write( "\n" ); document.write( "    - Inflation and Salary problems \r
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