document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=315557>Question 315557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Interest Compounded Continuously. <BR>\n" );
document.write( "Suppose that Po is invested in a savings account where interest is compounded continuity at 3.1% per year. \r<BR>\n" );
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document.write( "A. Express P(t) in terms of Po and 0.031. \r<BR>\n" );
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document.write( "B. Suppose that $1000 is invested. What is the balance after 1 yr? After 2yrs? \r<BR>\n" );
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document.write( "C. When will an investment of $1000 double itself?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225790 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=225790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "A.\r<BR>\n" );
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document.write( "In general:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(t)\ =\ P_oe^{rt}\">\r<BR>\n" );
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document.write( "For a 3.1% interest rate:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(t)\ =\ P_oe^{0.031t}\">\r<BR>\n" );
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document.write( "B.  1 yr:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(1)\ =\ 1000e^{0.031}\">\r<BR>\n" );
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document.write( "B.  2 yr:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(2)\ =\ 1000e^{0.031\,\cdot\,2}\">\r<BR>\n" );
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document.write( "The calculator work is left as an exercise for the student.\r<BR>\n" );
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document.write( "C.  The investment will double regardless of the value of the initial investment when <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{P(t)}{P_o}\ =\ 2\">, which is to say when, in general,  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{rt}\ =\ 2\">, or specifically for this problem, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{0.031t}\ =\ 2\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ e^{rt}\ =\ 2\">\r<BR>\n" );
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document.write( "Take the natural log of both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(e^{rt}\right)\ =\ \ln(2)\">\r<BR>\n" );
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document.write( "Use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log_b(x^n)\ =\ n\log_b(x)\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ rt\ln\left(e\right)\ =\ \ln(2)\">\r<BR>\n" );
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document.write( "Use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE ln(e)\ =\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ rt\ =\ \ln(2)\">\r<BR>\n" );
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document.write( "Divide by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{\ln(2)}{r}\">\r<BR>\n" );
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document.write( "Is the general solution.  The specific solution and the resulting arithmetic are left as an exercise for the student.\r<BR>\n" );
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document.write( "In a still more general case, the time, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\">, to multiply the principal amount by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE m\">, with interest rate, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r\">, compounded continuously is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{\ln(m)}{r}\">\r<BR>\n" );
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document.write( "By the way, this was 4 problems in one post.  You are allowed only 1 problem per post.  Read the instructions, that's why they are there.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
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