document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144422>Question 144422</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tutors I submitted this once showing my work but I can't find my notes. If you sear your email you will see how I worked the problem.  I asked if you could check my work.  Here is the word problem again..Thank you $5000 is invested at interest rate K, compounded continuously and grows to $6954.84 in 6 years.  Find the interest rate; the exponential growth function; the balance after 10 years and find the doubling time.  \r<BR>\n" );
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document.write( "If I remember my notes I think I had the doubling time as 12 years, the interest rate at 6%.\r<BR>\n" );
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document.write( "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 #105358 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=105358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> $5000 is invested at interest rate K, compounded continuously and grows to $6954.84 in 6 years. Find the interest rate; the exponential growth function; the balance after 10 years and find the doubling time. <BR>\n" );
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document.write( "P*e^rt = A<BR>\n" );
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document.write( "5000*e^6r = 6954.84<BR>\n" );
document.write( "e^6r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6954.84%2F5000 ALIGN=MIDDLE  ALT=\"6954.84%2F5000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 5000<BR>\n" );
document.write( "e^6r = 1.390968<BR>\n" );
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document.write( "Find the nat log of both sides:<BR>\n" );
document.write( "ln(e^6r) = 1.390968<BR>\n" );
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document.write( "log equiv of exponents<BR>\n" );
document.write( "6r*ln(e) = ln(1.390698)<BR>\n" );
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document.write( "Find the ln of both sides (ln(e) = 1)<BR>\n" );
document.write( "6r = .33000<BR>\n" );
document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.33%2F6 ALIGN=MIDDLE  ALT=\".33%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "r = .055, 5.5%<BR>\n" );
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document.write( "Growth function<BR>\n" );
document.write( "f(t) = 5000*e^.055t<BR>\n" );
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document.write( "use this to check above solution on a calc: enter: 5000*e^(.055*6) = 6954.84<BR>\n" );
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document.write( "the balance after 10 years<BR>\n" );
document.write( "A = 5000*e^(.055*10)<BR>\n" );
document.write( "A = 8666.26<BR>\n" );
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document.write( " and find the doubling time.<BR>\n" );
document.write( "1*e^.055t = 2<BR>\n" );
document.write( ".055t*ln(e) = ln(2)<BR>\n" );
document.write( ".055t = .693147<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.693147%2F.055 ALIGN=MIDDLE  ALT=\".693147%2F.055\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 12.6 yrs<BR>\n" );
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document.write( "Check this using the value of 5000 on calc: enter 5000*e^(.055*12.6) = 9998.53 ~ 10000  </SPAN>\n" );
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