document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=447946>Question 447946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a city is growing exponentially. Initially the population was 43,000 while 7 years later the population was 79,700. Find\r<BR>\n" );
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document.write( "the population 4 years later (11 years from the beginning)\r<BR>\n" );
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document.write( "and the doubling time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #308299 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=308299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The population of a city is growing exponentially. Initially the population was 43,000 while 7 years later the population was 79,700. <BR>\n" );
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document.write( "Find the population 4 years later (11 years from the beginning) <BR>\n" );
document.write( "and the doubling time.<BR>\n" );
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document.write( "p = ab^t<BR>\n" );
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document.write( "Solve for a and b:<BR>\n" );
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document.write( "Initial conditions (0,43000) so a = 43000<BR>\n" );
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document.write( "p(7) = 43000*b^7 = 79,700<BR>\n" );
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document.write( "Divide by 43000 and solve for \"b\":<BR>\n" );
document.write( "b^7 = 1.8535<BR>\n" );
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document.write( "b = 1.0922<BR>\n" );
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document.write( "p(t) = 43000*(1.0922)^t<BR>\n" );
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document.write( "Find the population 4 years later (11 years from the beginning)<BR>\n" );
document.write( "p(11) = 43000*(1.0922)^11 = 113,395.39<BR>\n" );
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document.write( "and the doubling time.<BR>\n" );
document.write( "Solve 1.0922^t = 2<BR>\n" );
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document.write( "t*log(1.0922) = log(2)<BR>\n" );
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document.write( "t = 7.86 years<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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