document.write( "Question 1153619: The population P of a fish farm in t years is modeled by the equation
\n" ); document.write( "P(t) =
\n" ); document.write( "2000/1 + 9e exponent is −0.6t
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\n" ); document.write( "To the nearest tenth, how long will it take for the population to reach 900? \n" ); document.write( "
Algebra.Com's Answer #775873 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Plug in P(t) = 900 and solve for t
\n" ); document.write( "P(t) = 2000/(1 + 9*e^(-0.6*t))
\n" ); document.write( "900 = 2000/(1 + 9*e^(-0.6*t))
\n" ); document.write( "900(1 + 9*e^(-0.6*t)) = 2000
\n" ); document.write( "900*1 + 900*9*e^(-0.6*t) = 2000
\n" ); document.write( "900 + 8100*e^(-0.6*t) = 2000
\n" ); document.write( "8100*e^(-0.6*t) = 2000-900
\n" ); document.write( "8100*e^(-0.6*t) = 1100
\n" ); document.write( "e^(-0.6*t) = (1100)/(8100)
\n" ); document.write( "e^(-0.6*t) = 0.135802469135802
\n" ); document.write( "Ln( e^(-0.6*t) ) = Ln( 0.135802469135802 )
\n" ); document.write( "-0.6*t*Ln( e ) = Ln( 0.135802469135802 )
\n" ); document.write( "-0.6*t*1= -1.99655388187407
\n" ); document.write( "-0.6*t= -1.99655388187407
\n" ); document.write( "t= (-1.99655388187407)/(-0.6)
\n" ); document.write( "t= 3.32758980312345\r
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\n" ); document.write( "\n" ); document.write( "If we plug t= 3.32758980312345 into the function, we get
\n" ); document.write( "P(t) = 2000/(1+9*e^(-0.6*t))
\n" ); document.write( "P(3.32758980312345) = 2000/(1+9*e^(-0.6*3.32758980312345))
\n" ); document.write( "P(3.32758980312345) = 2000/(1+9*e^(-1.99655388187407))
\n" ); document.write( "P(3.32758980312345) = 2000/(1+9*0.135802469135802)
\n" ); document.write( "P(3.32758980312345) = 2000/(1+1.22222222222222)
\n" ); document.write( "P(3.32758980312345) = 2000/(2.22222222222222)
\n" ); document.write( "P(3.32758980312345) = 900.000000000001
\n" ); document.write( "which is really really close to 900. The error is due to rounding\r
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\n" ); document.write( "\n" ); document.write( "When rounding 3.32758980312345 to the nearest tenth, you should get 3.3\r
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\n" ); document.write( "\n" ); document.write( "So the answer is approximately 3.3 years
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