\r\n" );
document.write( "In a lake, there is a patch of lily pads. Every day the patch doubles in size. If it takes 48 days for the patch to cover\r\n" );
document.write( "the entire lake, how long would it take for the patch to cover half of the lake? \r\n" );
document.write( "\r\n" );
document.write( "I wholeheartedly agree with Tutor @Ikleyn that the patch will take 47 days to cover 
of the lake, considering\r\n" );
document.write( "that its growth DOUBLES every day.\r\n" );
document.write( "\r\n" );
document.write( "For this exponential growth scenario, we need to use the Simple Discrete Growth Formula: 
, or 
, where: \r\n" );
document.write( " f(x) = Growth percent/fraction at a particular time (max being 100, or 1, or 
)\r\n" );
document.write( " x = time period during growth\r\n" );
document.write( " a = Initial/Beginning growth percent/fraction (
)\r\n" );
document.write( " b = growth rate <=== this can also be represented by 1 + r \r\n" );
document.write( " \r\n" );
document.write( "
---- Substituting 48 for x, and 2 for b\r\n" );
document.write( " 
---- Substituting 1 (100%) for f(48)\r\n" );
document.write( "Initial percent/fraction of lake covered, or a = 
\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( " 
----- Substituting for a, and 2 for b\r\n" );
document.write( " 
----- Substituting for f(x)\r\n" );
document.write( " 
-- Converting to 
, and to 
\r\n" );
document.write( " 
\r\n" );
document.write( " - 1 = - 48 + x ----- BASES are equal, and so are the exponents\r\n" );
document.write( "\r\n" );
document.write( "Time it takes for the patch to cover of the lake, or x = - 1 + 48 = 47 days.
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
