document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468306>Question 468306</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you invest $130 at 4% compounded continuously.<BR>\n" );
document.write( "a. Write an exponential function to model the amount in your investment account.<BR>\n" );
document.write( "b. Explain what each value in the function model represents.<BR>\n" );
document.write( "c. In how many years will the total reach $600? Show your work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321321 by </B><A HREF=/tutors/aboutme.mpl?userid=Gogonati><B>Gogonati(855)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Gogonati><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=Gogonati><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The compounding continuously formula is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28t%29=P%2Ae%5E%28rt%29 ALIGN=MIDDLE  ALT=\"A%28t%29=P%2Ae%5E%28rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where P is the \r<BR>\n" );
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document.write( "initial investment, r is the interest rate, and t the amount of time in years the<BR>\n" );
document.write( "investment is held. To find in how many years the initial investment of $130 will<BR>\n" );
document.write( "reach $600, we substitute in our formula A(t)=600, and get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600=130%2Ae%5E%28.04t%29 ALIGN=MIDDLE  ALT=\"600=130%2Ae%5E%28.04t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, solving this equation we get:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=13%2Ae%5E%28.04t%29 ALIGN=MIDDLE  ALT=\"60=13%2Ae%5E%28.04t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><=>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F13=e%5E%28.04t%29 ALIGN=MIDDLE  ALT=\"60%2F13=e%5E%28.04t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, taking the natural logarithms of both sides, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2860%2F13%29=.04t ALIGN=MIDDLE  ALT=\"ln%2860%2F13%29=.04t\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and final <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28ln%2860%2F13%29%29%2F.04 ALIGN=MIDDLE  ALT=\"t=%28ln%2860%2F13%29%29%2F.04\"   DISABLED_style= \"max-width:90%; height:auto;\" > or t=38 years. </SPAN>\n" );
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