document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=393385>Question 393385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Exoponential Method<BR>\n" );
document.write( "1.A biologist is researching a newly-discovered species of bacteria. at time t=0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Find an exponential equation thet approximates the information.\r<BR>\n" );
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document.write( "2. A $1,000 deposit is made at a bank that pays 12% compound monthly. How much will you havein your account at the end of 10 years.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #279211 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=279211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.A biologist is researching a newly-discovered species of bacteria.<BR>\n" );
document.write( " at time t=0 hours, he puts one hundred bacteria into what he has determined to<BR>\n" );
document.write( " be a favorable growth medium.<BR>\n" );
document.write( " Six hours later, he measures 450 bacteria.<BR>\n" );
document.write( " Find an exponential equation that approximates the information.<BR>\n" );
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document.write( "find k, the growth factor<BR>\n" );
document.write( "100*(2^(6/k)) = 450<BR>\n" );
document.write( "Divide both sides by 100<BR>\n" );
document.write( "2^(6/k) = 4.5<BR>\n" );
document.write( "use logs here<BR>\n" );
document.write( "log(2^(6/k)) = log(4.5)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fk ALIGN=MIDDLE  ALT=\"6%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" >log(2) = log(4.5)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fk ALIGN=MIDDLE  ALT=\"6%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284.5%29%2Flog%282%29 ALIGN=MIDDLE  ALT=\"log%284.5%29%2Flog%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fk ALIGN=MIDDLE  ALT=\"6%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.17<BR>\n" );
document.write( "k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F2.17 ALIGN=MIDDLE  ALT=\"6%2F2.17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "k = 2.765 is the growth factor<BR>\n" );
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document.write( "A = Ao*2^(t/2.765), the exponential equation<BR>\n" );
document.write( "where<BR>\n" );
document.write( "Ao = initial amt<BR>\n" );
document.write( "A = amt after t hrs<BR>\n" );
document.write( "t = time in hrs<BR>\n" );
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document.write( "Check equation using Ao = 100: In a calc enter: 100*2^(6/2.765) results: 450.0<BR>\n" );
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document.write( "2. A $1,000 deposit is made at a bank that pays 12% compound monthly.<BR>\n" );
document.write( " How much will you have in your account at the end of 10 years.<BR>\n" );
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document.write( "Compound interest formula:<BR>\n" );
document.write( "A =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%281%2Br%2Fn%29%5E%28nt%29%29 ALIGN=MIDDLE  ALT=\"p%281%2Br%2Fn%29%5E%28nt%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <BR>\n" );
document.write( "A = resulting amt after t years<BR>\n" );
document.write( "P = principal ($1000)<BR>\n" );
document.write( "r = interest rate in decimals (.12)<BR>\n" );
document.write( "n = no. of time compounded per yr (12 times/yr)<BR>\n" );
document.write( "t = no. of yrs (10 yrs)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%281%2B.12%2F12%29%5E%2812%2A10%29%29 ALIGN=MIDDLE  ALT=\"1000%281%2B.12%2F12%29%5E%2812%2A10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%281%2B.01%29%5E%28120%29%29 ALIGN=MIDDLE  ALT=\"1000%281%2B.01%29%5E%28120%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "A =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%281.01%29%5E%28120%29%29 ALIGN=MIDDLE  ALT=\"1000%281.01%29%5E%28120%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "on a calc<BR>\n" );
document.write( "A = $3300.39 </SPAN>\n" );
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