document.write( "Question 1204452: Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 2600 bacteria selected from this population reached the size of 2685 bacteria in one and a half hours. Find the hourly growth rate paramete \n" ); document.write( "

Algebra.Com's Answer #840717 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Suppose that the number of bacteria in a certain population increases according
\n" ); document.write( "to a continuous exponential growth model. A sample of 2600 bacteria selected
\n" ); document.write( "from this population reached the size of 2685 bacteria in one and a half hours.
\n" ); document.write( "Find the hourly growth rate paramete
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The exponential growth model is\r\n" );
document.write( "\r\n" );
document.write( "    N = ,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " is the initial population size, t is the time, \"b\" is the base of the exponential function.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For your problem,  = 2600, t= 1.5 hours, N= 2685, so the equation takes the form\r\n" );
document.write( "\r\n" );
document.write( "    2685 = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Only base \"b\" is an unknown.  To find b, make these standard manipulations, step by step\r\n" );
document.write( "\r\n" );
document.write( "     = \r\n" );
document.write( "\r\n" );
document.write( "    1.032692308 = \r\n" );
document.write( "\r\n" );
document.write( "    log(1.032692308) = 1.5*log(b)\r\n" );
document.write( "\r\n" );
document.write( "    log(b) =  = 0.009313961\r\n" );
document.write( "\r\n" );
document.write( "    b =  = 1.021677811\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The base, or the exponential hourly rate of growth in this problem is 1.021677811.\r\n" );
document.write( "\r\n" );
document.write( "         You may round it to 1.00931, for example.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );