document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270747>Question 270747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me with this problem..<BR>\n" );
document.write( "in 2005 consumers received an average of 3253 spam messages.the volume of spam messages is decreasing with an exponential decay rate of 13.7% per year.<BR>\n" );
document.write( "a--find th eexponential decay function that can be used to predict average number of spam messages m(t)+years after 2005.<BR>\n" );
document.write( "b--predict the number of spam messagesreceived per consumer in 2010.<BR>\n" );
document.write( "c--in what year will the average consumer receive 100 spam messages? </SPAN>\n" );
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document.write( "in 2005 consumers received an average of 3253 spam messages.the volume of spam messages is decreasing with an exponential decay rate of 13.7% per year.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "If the decay rate is 13.7%, the survival rate is 86.3%<BR>\n" );
document.write( "---<BR>\n" );
document.write( "a--find th exponential decay function that can be used to predict average number of spam messages m(t)+years after 2005.<BR>\n" );
document.write( "A(t) = 3253(0.863)^t where t is the number of years after 2005<BR>\n" );
document.write( "--------------------------------------------------<BR>\n" );
document.write( "b--predict the number of spam messages received per consumer in 2010.<BR>\n" );
document.write( "A(5) = 3253(0.863)^5 = 1557.18<BR>\n" );
document.write( "Rounding up get A(5) is approximately 1558<BR>\n" );
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document.write( "c--in what year will the average consumer receive 100 spam messages?<BR>\n" );
document.write( "Solve for \"t\":<BR>\n" );
document.write( "100 = 3253(0.863)^t<BR>\n" );
document.write( "0.863^t = 0.06418<BR>\n" );
document.write( "t = log(0.06418)/log(0.863) = 18.64 yrs<BR>\n" );
document.write( "Round up: t = 19 yrs.<BR>\n" );
document.write( "==========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "========================== </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );