document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175529>Question 1175529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A new virus increases exponentially at the monthly rate of 2.8%. Four months<BR>\n" );
document.write( "after the initial outbreak, there were 10,000 reported cases. (Exponential<BR>\n" );
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document.write( "a. How many were initially infected with the virus?<BR>\n" );
document.write( "b. Model the number of reported case as a function of time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801159 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=801159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula you can use is:\r<BR>\n" );
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document.write( "f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the growth rate per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "in your problem:\r<BR>\n" );
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document.write( "f is equal to 10,000<BR>\n" );
document.write( "r is equal to .028 per month<BR>\n" );
document.write( "n is equal to 4 months.\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "10,000 = p * (1 + .028) ^ 4\r<BR>\n" );
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document.write( "solve for p to get:\r<BR>\n" );
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document.write( "p = 10,000 / (1 + .028) ^ 4 = 8954.215481.\r<BR>\n" );
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document.write( "confirm by replacing p in the original equatio n and solving for f.\r<BR>\n" );
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document.write( "equation becomes f = 8954.215481 * (1 + .028) ^ 4\r<BR>\n" );
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document.write( "solve for f to get:\r<BR>\n" );
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document.write( "f = 10,000.\r<BR>\n" );
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document.write( "this confirms the value of p is good.\r<BR>\n" );
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document.write( "the reported cases as a function of time is f = 8954.215481 * 1.28 ^ n\r<BR>\n" );
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document.write( "f is the future vlue.<BR>\n" );
document.write( "p is the present value which is equal to 8954.215481.<BR>\n" );
document.write( "r is equal to .028 per month.<BR>\n" );
document.write( "n is the number of months.\r<BR>\n" );
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document.write( "this equation can be graphed by replacing f with y and n with x.<BR>\n" );
document.write( "the graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/022101.jpg\" >\r<BR>\n" );
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document.write( "you can see that when x = 4, y = 10,000.\r<BR>\n" );
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document.write( "the growth is exponential.\r<BR>\n" );
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document.write( "when x = 36, y = 1.028^36 = 24198.01096 which is equal to 24198.011 when rounded to 3 decimal places, as shown on the graph.\r<BR>\n" );
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document.write( "the formula is exponential because it is of the form of y = a * b ^ x, with a = 8954.215481 and b = 1.028 and x = the exponent. </SPAN>\n" );
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