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	<title>007A Sample Midterm 3, Problem 2 - Revision history</title>
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	<updated>2026-04-20T23:16:00Z</updated>
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		<id>https://gradwiki.math.ucr.edu/index.php?title=007A_Sample_Midterm_3,_Problem_2&amp;diff=3982&amp;oldid=prev</id>
		<title>Kayla Murray: Created page with &quot;&lt;span class=&quot;exam&quot;&gt;Suppose the size of a population at time &amp;nbsp;&lt;math style=&quot;vertical-align: 0px&quot;&gt;t&lt;/math&gt;&amp;nbsp; is given by  ::&lt;math&gt;N(t)=\frac{1000t}{5+t},~t\ge 0.&lt;/math&gt;...&quot;</title>
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		<updated>2017-11-12T00:56:51Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt;Suppose the size of a population at time  &amp;lt;math style=&amp;quot;vertical-align: 0px&amp;quot;&amp;gt;t&amp;lt;/math&amp;gt;  is given by  ::&amp;lt;math&amp;gt;N(t)=\frac{1000t}{5+t},~t\ge 0.&amp;lt;/math&amp;gt;...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt;Suppose the size of a population at time &amp;amp;nbsp;&amp;lt;math style=&amp;quot;vertical-align: 0px&amp;quot;&amp;gt;t&amp;lt;/math&amp;gt;&amp;amp;nbsp; is given by&lt;br /&gt;
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::&amp;lt;math&amp;gt;N(t)=\frac{1000t}{5+t},~t\ge 0.&amp;lt;/math&amp;gt;&lt;br /&gt;
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&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt;(a) Determine the size of the population as &amp;amp;nbsp;&amp;lt;math style=&amp;quot;vertical-align: -1px&amp;quot;&amp;gt;t\rightarrow \infty.&amp;lt;/math&amp;gt;&amp;amp;nbsp; We call this the limiting population size.&lt;br /&gt;
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&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt;(b) Show that at time &amp;amp;nbsp;&amp;lt;math style=&amp;quot;vertical-align: -4px&amp;quot;&amp;gt;t=5,&amp;lt;/math&amp;gt;&amp;amp;nbsp; the size of the population is half its limiting size.&lt;br /&gt;
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[[007A Sample Midterm 3, Problem 2 Solution|'''&amp;lt;u&amp;gt;Solution&amp;lt;/u&amp;gt;''']]&lt;br /&gt;
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[[007A Sample Midterm 3, Problem 2 Detailed Solution|'''&amp;lt;u&amp;gt;Detailed Solution&amp;lt;/u&amp;gt;''']]&lt;br /&gt;
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[[007A_Sample_Midterm_3|'''&amp;lt;u&amp;gt;Return to Sample Exam&amp;lt;/u&amp;gt;''']]&lt;/div&gt;</summary>
		<author><name>Kayla Murray</name></author>
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