document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129690>Question 1129690</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At the beginning of 2010 Dana's car was worth $13,000, but the value of her car decreases exponentially. She notices that the value of her car decreases by 19% every 3 years. <BR>\n" );
document.write( "A)What is the 3-year growth factor for the value of Dana's car?<BR>\n" );
document.write( "B)What is the 1-year growth factor for the value of Dana's car?<BR>\n" );
document.write( "C)Write a function f that determines the value of Dana's car (in dollars) in terms of the number of years t since the beginning of 2010.\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 #746491 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=746491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula to use is f = p * (1 + r) ^ t\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 year<BR>\n" );
document.write( "t is the number of years\r<BR>\n" );
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document.write( "in 3 years, the car reduces 19% in value.\r<BR>\n" );
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document.write( "therefore, in 3 years, the value of the car is 13000 minus .19 * 3000 = 10530.\r<BR>\n" );
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document.write( "your frmula of f = p * (1 + r) ^ t becomes:\r<BR>\n" );
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document.write( "10530 = 13000 * (1 + r) ^ 3\r<BR>\n" );
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document.write( "divide both sides of this equation by 1000 to get:<BR>\n" );
document.write( "10530 / 13000 = 1 + r) ^ 3<BR>\n" );
document.write( "take the third root of both sides of this equation to get:<BR>\n" );
document.write( "(10530 / 13000) ^ (1/3) = 1 + r<BR>\n" );
document.write( "subtract 1 from both sides of this equation to get:<BR>\n" );
document.write( "(10530 / 13000) ^ (1/3) - 1 = r<BR>\n" );
document.write( "solve for r to get:<BR>\n" );
document.write( "r = -.0678302482\r<BR>\n" );
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document.write( "that's your annual growth rate.\r<BR>\n" );
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document.write( "your formula becomes:\r<BR>\n" );
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document.write( "f = 13000 * (1 - .0678302482) ^ t\r<BR>\n" );
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document.write( "in 1 year, the value of the car is 13000 * (1 - .0678302482) ^ 1 = 12118.20677.<BR>\n" );
document.write( "in 2 years, the value of the car is 13000 * (1 - .0678302482) ^ 2 = 11296.2258.<BR>\n" );
document.write( "in 3 years, the value of the car is 13000 * (1 - .0678302482) ^ 3 = 10530.\r<BR>\n" );
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document.write( "the 3 year growth factor is (1 - .0678302482) ^ 3 = .81<BR>\n" );
document.write( "the 1 year growth factor is (1 - .0678302482) ^ 1 = .9321697518\r<BR>\n" );
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document.write( "the formula to find the value of the car after t years is f = 13000 * (1 - .0678302482) ^ t\r<BR>\n" );
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document.write( "that formula can be graphed as shown below.<BR>\n" );
document.write( "the formula to graph is y = 13000 * (1 - .0678302482) ^ x.<BR>\n" );
document.write( "in the graph, y represents f and x represents t.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/112502.jpg\" alt=\"$$$\" >\r<BR>\n" );
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