document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=718152>Question 718152</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve for A and B in this exponential decay model y= ae^-bx. I have the following points: when x=0.6, y=1000 and when x=1.8, y=1.\r<BR>\n" );
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document.write( "I have done the following but I am not convienced it is the right path...\r<BR>\n" );
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document.write( "y=ae-bx therefor e-bx=y/a ... take log e of both sides ... loge e-bx = loge y/a\r<BR>\n" );
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document.write( "but logee=1 therefor -bx=loge y/a ... move the x over to get -b=x loge y/a\r<BR>\n" );
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document.write( "then enter values for x and y from example 1... -b= (0.6) loge(1000/a)\r<BR>\n" );
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document.write( "Is this the correct path to take for solving this?? Any advice would be greafull appreciated. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #853677 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13292)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=853677\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The function has the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ae%5E%28-bx%29 ALIGN=MIDDLE  ALT=\"y=ae%5E%28-bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The two given data points are (0.6,1000) and (1.8,1), giving us these two equations:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=ae%5E%28-0.6b%29 ALIGN=MIDDLE  ALT=\"1000=ae%5E%28-0.6b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=ae%5E%28-1.8b%29 ALIGN=MIDDLE  ALT=\"1=ae%5E%28-1.8b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Dividing the first equation by the second will eliminate a, giving us an equation we can solve to find b.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=e%5E%281.2b%29 ALIGN=MIDDLE  ALT=\"1000=e%5E%281.2b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281000%29=1.2b ALIGN=MIDDLE  ALT=\"ln%281000%29=1.2b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=ln%281000%29%2F1.2%29 ALIGN=MIDDLE  ALT=\"b=ln%281000%29%2F1.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A calculator then gives the value of b to several decimal places as 5.75646...<br><BR>\n" );
document.write( "Use that value of b in the second equation to get an equation we can solve to find the value of a.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=ae%5E%28-1.8b%29 ALIGN=MIDDLE  ALT=\"1=ae%5E%28-1.8b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1%2Fe%5E%28-1.8b%29=e%5E%281.8b%29 ALIGN=MIDDLE  ALT=\"a=1%2Fe%5E%28-1.8b%29=e%5E%281.8b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Using a calculator then gives the value of a to several decimal places as 31622.7766....<br><BR>\n" );
document.write( "ANSWERS (to several decimal places):<BR>\n" );
document.write( "a = 31622.7766<BR>\n" );
document.write( "b = 5.75646<br><BR>\n" );
document.write( "Graphing this function on a graphing calculator confirms the two given data points (0.6,1000) and (1.8,1).<br><BR>\n" );
document.write( "Found using a different path than that used by the other tutor, this matches his answers -- except that currently he has a typo in the leading digit of the value for a.<br><BR>\n" );
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