document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=569384>Question 569384</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!!!! I will praise you!!!<BR>\n" );
document.write( "    At 9:30 am tomorrow, we open our doors for the last time. The price of every item in the store will be reduced 10% every hour, on the hour, beginning at 10am until everything goes, The stereo calvin would love to buy is $359 dollars.. Calvin has saved $270 for the stereo. Henry told calvin that at 11:01 am, the price of the stereo will be $287.20. Jacob says $290.79 will be the price. What might he expect the price to be at 11:01 and why? Henry claims that since the prices go down 105 every hour, after 10 hours, the stereo will be free. He tells calvin to arrive at the store at 8pm for a free stereo. Do you agree with Henry's reasoning? Explain why and why not. Sales tax is 6%. Assuming he gets no more money, explain to Calvin when he will be able to afford the stereo and how you figured this out. Be sure your work is shown in an organized format so that it can be easily followed\r<BR>\n" );
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document.write( "THANKS SOO MUCH!!!!!!!!!!!!!!!!! :DDDDDDDDDDDDDDDD </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367317 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=367317\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The total amount to be paid after the first 10% reduction (considering the 6% sales tax) is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 359\ \times\ 0.9\ \times 1.06\">\r<BR>\n" );
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document.write( "The second hour\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (359\ \times\ 0.9)\ \times\ 0.9\ \times\ 1.06\">\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 359\ \times\ (0.9)^2\ \times\ 1.06\">\r<BR>\n" );
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document.write( "and, in general, after <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> hours:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (359)(0.9)^t(1.06)\">\r<BR>\n" );
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document.write( "Since Calvin's funds are limited to $270.00, we need to solve\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (359)(0.9)^t(1.06)\ <\ 270\">\r<BR>\n" );
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document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> and round up to the next higher integer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (0.9)^t\ =\ \frac{270}{(359)(1.06)}\ \approx\ 0.709\">\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(0.9)^t\ \approx\ \ln(0.709)\">\r<BR>\n" );
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document.write( "Use\r<BR>\n" );
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document.write( "<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( "to write\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ln(0.9)\ \approx\ \ln(0.709)\">\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ \approx\ \frac{\ln(0.709)}{\ln(0.9)}\ \approx\ 3.25\">\r<BR>\n" );
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document.write( "Round up\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ 4\">\r<BR>\n" );
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document.write( "So the total amount will be less than Calvin's $270 right after the fourth hour.  10 is the first hour, 11 is the second hour...\r<BR>\n" );
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document.write( "So Calvin needs to come in at 1:00 pm when the total amount will be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (359)(0.9)^4(1.06)\ \approx\ $249.67\">\r<BR>\n" );
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document.write( "Which means that Calvin can go to lunch as long as he doesn't spend more than <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large $20.33\"> for his meal including tax and tip.\r<BR>\n" );
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document.write( "The only flaw in Calvin's plan is: What if there are a limited number of these stereo sets -- a number less than or equal to the number of people who come in at noon with $280 in their pocket?  In such an event, Calvin is out of luck.\r<BR>\n" );
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document.write( "And by the way, Henry is an idiot.  You take 10% off the CURRENT price, not the FULL price, each hour.\r<BR>\n" );
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document.write( "<i><b>Super Double Plus Extra Credit</b></i>\r<BR>\n" );
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document.write( "Theoretically, the price will never reach zero since after any reduction, 90 percent of the previous amount remains.  However, a point will be reached eventually such that the total amount, including tax, will be reduced to an amount when rounded to the nearest one cent will be $0.00.  Using the process outlined above, how many hours must elapse before he would actually receive the item absolutely free?  Hint: What value of <i><b>t</b></i> makes the total price less than $0.005?\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( "My calculator said it, I believe it, that settles it<BR>\n" );
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