document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207489>Question 1207489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An insect population grows every day. The growth rate of the number of insects per day is described by the function i(t) = 100. e^0.2t, where t is the number of days counted from a certain moment. Calculate using ICT but NOTE the calculation that you make with ICT!<BR>\n" );
document.write( "a) By how many insects has the population grown during the first ten days?<BR>\n" );
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document.write( "b) By how many insects has the population grown on the eleventh day?<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 #845400 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52790)</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=845400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "Hello, &nbsp;in this my post, &nbsp;I will not make calculations for you, &nbsp;using &nbsp;ICT, &nbsp;because &nbsp;I don't know what &nbsp;ICT &nbsp;is.<BR>\n" );
document.write( "And, &nbsp;in general, &nbsp;it is out of my principles of tutoring to make somebodies' job, &nbsp;which is pressing buttons,<BR>\n" );
document.write( "since it has no any relation to teaching. &nbsp;Making students' job, substituting students in pressing<BR>\n" );
document.write( "buttons is the worst possible tutors service which &nbsp;I &nbsp;can imagine - so, &nbsp;I &nbsp;never do it.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;My post is about another issue. &nbsp;I simply want to explain you\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;what your problem is about and, conceptually, &nbsp;what you should do with it.\r<BR>\n" );
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document.write( "If the function &nbsp;i(t) = 100.e((0.2t) &nbsp;is the growth rate, &nbsp;as it is written in your post,<BR>\n" );
document.write( "it literally means that the population function is the integral of it, &nbsp;i.e. the anti-derivative of this function.\r<BR>\n" );
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document.write( "Anti-derivative of &nbsp;&nbsp;i(t) = 100.e^(0.2t) &nbsp;&nbsp;is &nbsp;&nbsp;N(t) = 500.e^(0.2t)&nbsp;&nbsp;(plus, formally, &nbsp;a constant).\r<BR>\n" );
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document.write( "It means that calculations in the posts of other tutors &nbsp;(both &nbsp;@josgatithmetic and &nbsp;@Theo) &nbsp;are &nbsp;INCORRECT &nbsp;and &nbsp;IRRELEVANT.\r<BR>\n" );
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document.write( "They are irrelevant, &nbsp;since they &nbsp;MISTAKENLY &nbsp;treat the given growth rate function &nbsp;i(t) &nbsp;as a population function &nbsp;N(t).\r<BR>\n" );
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document.write( "So, &nbsp;again, &nbsp;the calculations in their posts are not consistent with wording in your post.\r<BR>\n" );
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document.write( "This discrepancy is that fundamental danger moment which I want to point/(to warn)/(to aware) you.\r<BR>\n" );
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document.write( "Next, to answer first question, you have two options, or two ways.\r<BR>\n" );
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document.write( "First way is to calculate &nbsp;10 &nbsp;values &nbsp;&nbsp;i(1), &nbsp;i(2), &nbsp;i(3), . . . , &nbsp;i(10) &nbsp;separately and then add all of them.\r<BR>\n" );
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document.write( "        You may round each value on the way, or round the final sum \r\n" );
document.write( "        - I do not think that it makes any serious difference.\r\n" );
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document.write( "Notice that the sequence &nbsp;i(1), &nbsp;i(2), &nbsp;i(3), . . . , &nbsp;i(10) &nbsp;is a geometric progression,<BR>\n" );
document.write( "so you can use the formula for the sum of geometric progression.\r<BR>\n" );
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document.write( "Second way is to calculate &nbsp;&nbsp;N(10) - N(0), &nbsp;using the population function.\r<BR>\n" );
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document.write( "To answer second question, &nbsp;simply calculate &nbsp;i(11) &nbsp;and round it.\r<BR>\n" );
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document.write( "In his post, regarding my writing, @greenestamps positions himself as a person,<BR>\n" );
document.write( "who can read in the head of visitors. Perhaps, he has such super-skills, but I don't.\r<BR>\n" );
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document.write( "Moreover, I am even not going to do it.\r<BR>\n" );
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document.write( "I react as I read, and I read what I see. My reaction was perfectly adequate to the posted problem.\r<BR>\n" );
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document.write( "I re-read the incoming post again. I see there this written text\r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\"The growth rate of the number of insects per day is described by the function i(t) = 100. e^0.2t\".\r<BR>\n" );
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document.write( "OK, I may assume that the person made a typo or a mistake saying \"the growth rate\" instead of \"population\",<BR>\n" );
document.write( "but next he writes \"per day\", highlighting the idea and clearly showing that it is really \"the growth rate\" <BR>\n" );
document.write( "and is not a typo or mistake.\r<BR>\n" );
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document.write( "So, I really do not understand why I should treat it in another way.\r<BR>\n" );
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document.write( "Only because @greenestamps wants it ?\r<BR>\n" );
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document.write( "<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Resume: &nbsp;&nbsp;My solution is ABSOLUTELY CORRECT * * * * *</H3><H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Comment from @greenestamps is ANSOLUTELY WRONG.</H3>\r<BR>\n" );
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