document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=824792>Question 824792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> [ A mosquito population doubles every 7 days if there were 5 mosquitoes initially, after how many days will the population contain 80 mosquitoes? ]\r<BR>\n" );
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document.write( "Thanks so much in advance:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #496765 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=496765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "exponential growth:<BR>\n" );
document.write( "y(t) = a * e^(kt)<BR>\n" );
document.write( "where y(t) = value at time t<BR>\n" );
document.write( "a = value at the start<BR>\n" );
document.write( "k = rate of growth (when k>0) or decay (when k<0)<BR>\n" );
document.write( "t = time<BR>\n" );
document.write( "---<BR>\n" );
document.write( "200% of any initial amount will be present after 7 days:<BR>\n" );
document.write( "arbitrarily choose 1 as the initial amount.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y(7) = 200 = 100 * e^(k7)<BR>\n" );
document.write( "2/1 = e^(k7)<BR>\n" );
document.write( "2 = e^(k7)<BR>\n" );
document.write( "ln(2) = ln(e^(k7))<BR>\n" );
document.write( "0.693147180559945 = k7<BR>\n" );
document.write( "k = 0.693147180559945/7<BR>\n" );
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document.write( "k = 0.099021025794278<BR>\n" );
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document.write( "y(?) = 80 = 5 * e^(kt)<BR>\n" );
document.write( "80 = 5 * e^(kt)<BR>\n" );
document.write( "16 = e^(kt)<BR>\n" );
document.write( "ln(16) = ln(e^(kt))<BR>\n" );
document.write( "2.772588722239781 = kt<BR>\n" );
document.write( "t = 2.772588722239781/k<BR>\n" );
document.write( "t = 28<BR>\n" );
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document.write( "answer:<BR>\n" );
document.write( "the population will grow from 5 to 80 mosquitoes in 28 days<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php </SPAN>\n" );
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