document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212789>Question 212789</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the problem.\r<BR>\n" );
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document.write( "A rare baseball card was sold in 1990 for $285,000. The card was then resold in 1998 for $459,000. Assume that the card's value increases exponentially, and find an exponential function V(t) that fits the data. (Round decimals to three places.) (Points: 5)\r<BR>\n" );
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document.write( "These are my options\r<BR>\n" );
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document.write( "       V(t) = 285e0.766t, where t is the number of years after 1990.<BR>\n" );
document.write( "       V(t) = 285e0.06t, where t is the number of years after 1990.<BR>\n" );
document.write( "       V(t) = 285,000e0.766t, where t is the number of years after 1990.<BR>\n" );
document.write( "       V(t) = 285,000e0.06t, where t is the number of years after 1990.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161025 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=161025\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rare baseball card was sold in 1990 for $285,000. The card was then resold in 1998 for $459,000. Assume that the card's value increases exponentially, and find an exponential function V(t) that fits the data. (Round decimals to three places.) (Points: 5)<BR>\n" );
document.write( "These are my options<BR>\n" );
document.write( "V(t) = 285e0.766t, where t is the number of years after 1990.<BR>\n" );
document.write( "V(t) = 285e0.06t, where t is the number of years after 1990.<BR>\n" );
document.write( "V(t) = 285,000e0.766t, where t is the number of years after 1990.<BR>\n" );
document.write( "V(t) = 285,000e0.06t, where t is the number of years after 1990. <BR>\n" );
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document.write( "\"current value\" = \"initial value\" * e^(kt)<BR>\n" );
document.write( "V(t) = Ie^(kt)<BR>\n" );
document.write( "where<BR>\n" );
document.write( "I is the initial worth in dollars<BR>\n" );
document.write( "k is constant of variation<BR>\n" );
document.write( "t is time (in years)<BR>\n" );
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document.write( "We need to find 'k' based on the given data.  Plug in what we know and solve for 'k':<BR>\n" );
document.write( "V(t) = Ie^(kt)<BR>\n" );
document.write( "459000 = 285000e^(8k)<BR>\n" );
document.write( "459000/285000 = e^(8k)<BR>\n" );
document.write( "ln(459000/285000) = 8k<BR>\n" );
document.write( "ln(459000/285000)/8 = k<BR>\n" );
document.write( "0.060 = k<BR>\n" );
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document.write( "Therefore your equation is:<BR>\n" );
document.write( "V(t) = 285,000e0.06t, where t is the number of years after 1990. \r<BR>\n" );
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