document.write( "Question 617971: Solve the problem.\r
\n" ); document.write( "\n" ); document.write( "The logistic growth function f(t) = 400/1+9.0e-0.22t describes the population of a species of butterflies after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 12 months? \n" ); document.write( "

Algebra.Com's Answer #388655 by Theo(13342) $\"\"$ $\"About$

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based on this equation, the limiting size appears to be 400, assuming the equation is:
\n" ); document.write( "f(t) = 400 / (1+9.0*e^(-.22t))
\n" ); document.write( "presumably t represents number of months.
\n" ); document.write( "i'll assume that.
\n" ); document.write( "the following table of values based on the assumed equation is shown below:
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\r\n" );
document.write( "x       y = 400 / (1+9*e^(-.22t))\r\n" );
document.write( "0       40\r\n" );
document.write( "1       49\r\n" );
document.write( "2       59\r\n" );
document.write( "12      244 *****\r\n" );
document.write( "24      383\r\n" );
document.write( "36      399\r\n" );
document.write( "38      400\r\n" );
document.write( "

\n" ); document.write( "after 38 months the rounded up number stabilize at 400 and go no higher.
\n" ); document.write( "this is the maximum size of the population based on the equation.
\n" ); document.write( "a graph of this equation looks like this:
\n" ); document.write( " $\"graph%28600%2C600%2C-10%2C50%2C-20%2C500%2C400%2F%281%2B9%2Ae%5E%28-.22x%29%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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