document.write( "Question 278305: A population doubles in size every 15 years. Assuming exponential growth, find the annual growth rate and and continuous growth rate.\r
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Algebra.Com's Answer #202640 by ankor@dixie-net.com(22740)\"\" \"About 
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A population doubles in size every 15 years.
\n" ); document.write( " Assuming exponential growth, find the annual growth rate and and continuous growth rate.
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\n" ); document.write( "Assume an initial amt of 1, then results are 2
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\n" ); document.write( "Let x = per cent in decimal form growth rate per year
\n" ); document.write( "1(1+x)^15 = 2
\n" ); document.write( "ln((1+x)^15) = ln(2)
\n" ); document.write( "15*ln(1+x) = .693
\n" ); document.write( "ln(x+1) = \".693%2F15\"
\n" ); document.write( "ln(x+1) = .04621
\n" ); document.write( "find the antilog (e^x on calc)
\n" ); document.write( "x+1 = 1.0473
\n" ); document.write( "x = 1.0473 - 1
\n" ); document.write( "x = .0473 or 4.73 % annual growth rate
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\n" ); document.write( "Check on a calc: enter 1.0473^15 = 2.000
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\n" ); document.write( "Continuous growth rate
\n" ); document.write( "1*e^(15x) = 2
\n" ); document.write( "ln(e^15x) = ln(2)
\n" ); document.write( "15x*ln(e) = ln(2)
\n" ); document.write( "ln(e) = 1 so we have
\n" ); document.write( "15x = .693
\n" ); document.write( "x = \".693%2F15\"
\n" ); document.write( "x = .0462 or 4.62 % growth continuously
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\n" ); document.write( "Check on a calc: enter e^(.0462*15) = 1.99997 ~ 2 \n" ); document.write( "
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