document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173163>Question 1173163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The weight of bacteria in a culture t hours after it has been established is given by <BR>\n" );
document.write( "W= 2.5 .2^0.04t grams<BR>\n" );
document.write( "After what time will the weight reach:<BR>\n" );
document.write( "a  4grams.              b. 15 grams </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798346 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=798346\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation is:<BR>\n" );
document.write( "W = 2.5 * .2 ^ (0.04 * t) grams as far as i can tell.<BR>\n" );
document.write( "if that is correct, then the solution is found as follows:<BR>\n" );
document.write( "a)<BR>\n" );
document.write( "4 = 2.5 * .2 ^ (.04 * t)<BR>\n" );
document.write( "divide both sides of the equation by 2.5 to get:<BR>\n" );
document.write( "4/2.5 = .2 ^ (.04 * t)<BR>\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(4/2.5) = log(.2 ^ (.04 * t)) is equal to .04 * t * log(.2), the equation becomes:<BR>\n" );
document.write( "log(4/2.5) = .04 * t * log(.2)<BR>\n" );
document.write( "divide both sides of this equation by .04 * t to get:<BR>\n" );
document.write( "log(4/2.5) / log(.2) = .04 * t<BR>\n" );
document.write( "divide both sides of this equation by .04 to get:<BR>\n" );
document.write( "log(4/2.5) / log(.2) * 1/.04 = t<BR>\n" );
document.write( "solve for t to get:<BR>\n" );
document.write( "t = -949........<BR>\n" );
document.write( "this doesn't make sense, so there is pobably something wrong with the original equation.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "under the assumption that .2 really means * 2, i changed the original equation to be:<BR>\n" );
document.write( "W = 2.5 * 2 ^ (.04 * t)<BR>\n" );
document.write( "when W = 4, the equation becomes:<BR>\n" );
document.write( "4 = 2.5 * 2 ^ (.04 * t)<BR>\n" );
document.write( "divide both sides of this equation by 2.5 to get:<BR>\n" );
document.write( "4/2.5 = 2 ^ (.04 * t)<BR>\n" );
document.write( "take the log of both sides of this equation to get:<BR>\n" );
document.write( "log(4/2.5) = log(2 ^ (.04 * t))<BR>\n" );
document.write( "since log(2 ^ .04 * t)) is equal to .04 * t * log(2), the equation becomes:<BR>\n" );
document.write( "log(4/2.5) = .04 * t * log(2)<BR>\n" );
document.write( "divide both sides of the equation by log(2) to get:<BR>\n" );
document.write( "log(4/2.5) / log(2) = .04 * t<BR>\n" );
document.write( "divide both sides of this equation by .04 to get:<BR>\n" );
document.write( "log(4/2.5) / log(2) * 1 / .04 = t<BR>\n" );
document.write( "solve for t to get:<BR>\n" );
document.write( "t = 16.95179763\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "to solve for 15 grams, just replace W with 15 instead of 4 and do the same procedure.<BR>\n" );
document.write( "your answer should be 64.62406252.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "the original equation can be graphed and should show the same solutions rounded to at most 3 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/011605.jpg\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );