document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191778>Question 1191778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for t in terms of q for the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+q+=+1000%281%2F2%29%5E0.8%5Et+ ALIGN=MIDDLE  ALT=\"+q+=+1000%281%2F2%29%5E0.8%5Et+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823613 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=823613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think i have it now.<BR>\n" );
document.write( "i originally solved for q = 1000 * (1/2) ^ (.8 * t).<BR>\n" );
document.write( "that was wrong.<BR>\n" );
document.write( "the problem to be solved is q = 1000 * (1/2) ^ (.8 ^ t)<BR>\n" );
document.write( "at least that's what i think it is now.<BR>\n" );
document.write( "my calculator was not happy if there wasn't parentheses around the .8 ^ t.<BR>\n" );
document.write( "so, .....<BR>\n" );
document.write( "i am solving for q = 1000 * (1/2) ^ (.8 ^ t)\r<BR>\n" );
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document.write( "start with q = 1000 * (1/2) ^ (.8 ^ t)<BR>\n" );
document.write( "divide both sides of the equation by 10000 to get:<BR>\n" );
document.write( "q / 1000 = (1/2) ^ (.8 ^ t)<BR>\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(q/1000) = log((1/2)^(.8^t))<BR>\n" );
document.write( "since log(a^b) = b * log(a), this becomes:<BR>\n" );
document.write( "log(q/1000) = (.8^t)*log(1/2)<BR>\n" );
document.write( "divide both sides by log(1/2) to get:<BR>\n" );
document.write( "log(q/1000)/log(1/2) = .8^t<BR>\n" );
document.write( "take the log of both sides of this equation to get:<BR>\n" );
document.write( "log(log(q/1000)/log(1/2)) = log(.8^t)<BR>\n" );
document.write( "since log(a^b) = b*log(a), this becomes:<BR>\n" );
document.write( "log(log(q/1000)/log(1/2)) = t*log(.8)<BR>\n" );
document.write( "divide both sides of the equation by log(.8) to get:<BR>\n" );
document.write( "log(log(q/1000)/log(1/2))/log(.8) = t\r<BR>\n" );
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document.write( "i confirmed by replacing t with 20 in q = 1000 * (1/2) ^ (.8 ^ t) and got:<BR>\n" );
document.write( "q = 992.0404038.<BR>\n" );
document.write( "i then replaced q with 992.0404038 in log(log(q/1000)/log(1/2))/log(.8) = t and got:<BR>\n" );
document.write( "t = 20<BR>\n" );
document.write( "i graphed both equations by replacing q with y and t with x to show that they are equivalent to each other.<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/2022/030702.jpg\" >\r<BR>\n" );
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document.write( "the graph shows that the two equations are equivalent at x = 20<BR>\n" );
document.write( "this means at t = 20 in the original equation.\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo </SPAN>\n" );
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