document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169194>Question 169194</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Someone please help me with the following problem:\r<BR>\n" );
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document.write( "Suppose $5000 is invested at interest rate k, compounded continuously and grows to $6954.84 in 6 years.\r<BR>\n" );
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document.write( "(a)	Find the interest rate\r<BR>\n" );
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document.write( "(b)	Find the exponential growth function\r<BR>\n" );
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document.write( "(c)	Find the balance after 10 years\r<BR>\n" );
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document.write( "(d)	Find the doubling time\r<BR>\n" );
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document.write( "Thanks.\r<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 #124776 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=124776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Someone please help me with the following problem:<BR>\n" );
document.write( "Suppose $5000 is invested at interest rate k, compounded continuously and grows to $6954.84 in 6 years.<BR>\n" );
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document.write( "The continuous interest formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2Ae%5E%28rt%29 ALIGN=MIDDLE  ALT=\"P%2Ae%5E%28rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = A<BR>\n" );
document.write( "Where:<BR>\n" );
document.write( "P = initial amt (5000)<BR>\n" );
document.write( "r = interest rate in decimal form (k in this problem)<BR>\n" );
document.write( "t = time, in years (6yrs)<BR>\n" );
document.write( "A = final amt (6954.84)<BR>\n" );
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document.write( "(a) Find the interest rate<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%2Ae%5E%286k%29 ALIGN=MIDDLE  ALT=\"5000%2Ae%5E%286k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6954.84<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%286k%29 ALIGN=MIDDLE  ALT=\"e%5E%286k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%286k%29 ALIGN=MIDDLE  ALT=\"e%5E%286k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.390968; divided both sides by 5000<BR>\n" );
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document.write( "6k*ln(e) = ln(1.390968); find the nat log of both sides<BR>\n" );
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document.write( "6k = .33; nat log of e is 1<BR>\n" );
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document.write( "k = <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( "k = .055, 5.5% interest<BR>\n" );
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document.write( "Check on a calc: enter: 5000*e^(6*.055) = 6954.84<BR>\n" );
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document.write( "(b) Find the exponential growth function<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%2Ae%5E%28.055t%29 ALIGN=MIDDLE  ALT=\"5000%2Ae%5E%28.055t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(c) Find the balance after 10 years<BR>\n" );
document.write( "On a calc enter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%2Ae%5E%28%28.055%2A10%29%29 ALIGN=MIDDLE  ALT=\"5000%2Ae%5E%28%28.055%2A10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8666.27\r<BR>\n" );
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document.write( "(d) Find the doubling time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%2Ae%5E%28.055t%29 ALIGN=MIDDLE  ALT=\"5000%2Ae%5E%28.055t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10000; we want to find t here<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28.055t%29 ALIGN=MIDDLE  ALT=\"e%5E%28.055t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2F5000 ALIGN=MIDDLE  ALT=\"10000%2F5000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28.055%29 ALIGN=MIDDLE  ALT=\"e%5E%28.055%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2; <BR>\n" );
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document.write( ".055t*ln(e) = ln(2); find the nat log of both sides<BR>\n" );
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document.write( ".055t = .693; <BR>\n" );
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document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.693%2F.055 ALIGN=MIDDLE  ALT=\".693%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 on a calc: enter: 5000*e^(12.6*.055) = 9998.53 ~ 10000<BR>\n" );
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