document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144121>Question 1144121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help me please.  I do not know where to start. \r<BR>\n" );
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document.write( "1. Your doctor prescribes a daily 20 mg dose of a popular allergy medication, No-Drip. Roughly 24 hours after a first dose of the medicine is used, 40% of the No-Drip has been flushed from the body. You take 20 mg of No-Drip once a day. Make a table to show the maximum amount of No-Drip in your system each day for six days. Express each day's amount as a sum. Then, sketch a graph of the maximum No-Drip and the day number for at least fourteen days.<BR>\n" );
document.write( "2. Find the partial sum of the first seven terms in the series described in question 1.<BR>\n" );
document.write( "3. What do you notice about the graph of the amount of No-Drip in your system over fourteen days? What does this mean in the context of the problem? Confirm your claim analytically.<BR>\n" );
document.write( "4. Make a conjecture about the convergence of arithmetic and geometric series.<BR>\n" );
document.write( "5. Explore the sequence of partial sums for these three series using tables and graphs. In each case, will the series converge or diverge?<BR>\n" );
document.write( "6. Write a formula for the sum of a convergent geometric series with first term t1 and common ratio r, where |r| < 1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765120 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52798)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=765120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;As the given problem instructs you, &nbsp;solving it is the same as to go forward with closed eyes.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I will solve it by &nbsp;<U>MY &nbsp;WAY</U> : &nbsp;&nbsp;I will go with &nbsp;<U>OPENED &nbsp;EYES</U>.\r<BR>\n" );
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document.write( "<U>Solution</U>\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "         1-st day, 8:00 am  in the morning. You take 20 mg of the medication.\r\n" );
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document.write( "Next day, (day 2), 7:59 am. Of these 20 mg, only 1-0.4 = 0.6 of 20 mg, i.e, 0.6*20 mg remained in your body.\r\n" );
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document.write( "          2-nd day, 8:00 am in the morning. You take 20 mg of the medication.\r\n" );
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document.write( "Next day, (day 3), 7:59 am. Of these 20 mg, only 1-0.4 = 0.6 of 20 mg, i.e, 0.6*20 mg remained in your body.\r\n" );
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document.write( "                            Also, 0.6 of the previous day (of the day 2) still remains in your body, i.e. 0.6*(0.6*20) = 0.6^2*20 mg\r\n" );
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document.write( "                            In all, 0.6*20 + 0.6^2*20 = 20*(0.6+ 0.6^2) mg of the medication is at this time in your body.\r\n" );
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document.write( "And so on, and so on.\r\n" );
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document.write( "Even with non-armed eyes, you just see now a sum of an geometric progression with the first term of 20 mg  and the common ratio of 0.6:\r\n" );
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document.write( "    (n+1)-th day, at 7:59 am, before taking the medication,  the amount of the medication in your body is  \r\n" );
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document.write( "              A = 0.6*20 + 0.6^2*20 + . . . + 0.6^n*20 = 20*(0.6 + 0.6^2 + . . . 0.6^n)\r\n" );
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document.write( "    (n+1)-th day, at 8:00 am, after taking the medication,  the amount of the medication in your body is  \r\n" );
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document.write( "              B = 20 + 0.6*20 + 0.6^2*20 + . . . + 0.6^n*20 = 20*(1+0.6 + 0.6^2 + . . . 0.6^n).\r\n" );
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document.write( "Both expressions A and B are the sums of geometric progressions.\r\n" );
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document.write( "So, by knowing the formula for the sum of geometric progressions, you can complete the solution on your own (!)\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "At this point, &nbsp;I completed my explanations and instructions.\r<BR>\n" );
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document.write( "On geometric progressions, &nbsp;see introductory lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Geometric-progressions.lesson>Geometric progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-geometric-progressions.lesson>The proofs of the formulas for geometric progressions</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-geometric-progressions.lesson>Problems on geometric progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-geometric-progressions.lesson>Word problems on geometric progressions</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic <BR>\n" );
document.write( "<U>\"Geometric progressions\"</U>.\r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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