document.write( "Question 1194378: Suppose that an outbreak of cholera follows severe f;ooding in an isolated town of 2621 people, initially (Day0), 71 people are infected. Every day after, 12% of thoes still healthy fall ill.\r
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Algebra.Com's Answer #826576 by ikleyn(52795) $\"\"$ $\"About$

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\n" ); document.write( "Suppose that an outbreak of cholera follows severe flooding in an isolated town of 2621 people,
\n" ); document.write( "initially (Day0), 71 people are infected. Every day after, 12% of those still healthy fall ill.
\n" ); document.write( "By what day will 95% of the population be infected? (more specifically on the day before,
\n" ); document.write( "fewer than this number are infected, but on this day, the number or more are infected)
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\n" ); document.write( "\n" ); document.write( "            The solution by the other tutor is incorrect.\r
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\n" ); document.write( "\n" ); document.write( "            This problem requires attentive reading before solving.
\n" ); document.write( "            The governing formulas and the solution, as well as the answer are different
\n" ); document.write( "            from that of the other tutor.\r
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document.write( "Let H(n) be the number of healphy people at the day n  (those who are still healphy);\r\n" );
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document.write( "let I(n) be the number of ill people of the day n \r\n" );
document.write( "    (the cumulative sum of ill, formerly ill and death persons to the day n).\r\n" );
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document.write( "For the Day-0 we have, from the condition\r\n" );
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document.write( "    H(0) = 2621 - 71 = 2550;\r\n" );
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document.write( "    I(0) = 71\r\n" );
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document.write( "And in following days we have\r\n" );
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document.write( "    H(n) = (1-0.12)*H(n-1) = 0.88H(n-1),\r\n" );
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document.write( "    I(n) = 2621 - H(n),\r\n" );
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document.write( "in accordance with the problem's description.\r\n" );
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document.write( "Notice that these formulas and this setup are not the same as in the post by the other tutor:\r\n" );
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document.write( "    +------------------------------------------------------------------+\r\n" );
document.write( "    |    everyday decreasing the number of healthy people by 12%,      |\r\n" );
document.write( "    |        as described in the problem, is NOT THE SAME as           |                                                                   \r\n" );
document.write( "    |      everyday increasing the number of ill people by 12%.        |\r\n" );
document.write( "    +------------------------------------------------------------------+\r\n" );
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document.write( "Next, to solve the problem using formulas, notice that 95% of the population be infected means\r\n" );
document.write( "that 5% of 2621 is still healthy, or  0.05*2621 = 131 is healthy  (rounded).\r\n" );
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document.write( "So, we are looking to find n such that  H(n) =   is still greater than 131:\r\n" );
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document.write( "     >= 131.\r\n" );
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document.write( "To solve this inequality, divide both sides by 2550\r\n" );
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document.write( "     >=   = 0.05137;\r\n" );
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document.write( "take the logarithm base 10 of both sides\r\n" );
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document.write( "    n*log(0.88) >= log(0.05137)\r\n" );
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document.write( "express and calculate \"n\"\r\n" );
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document.write( "    n >=  = 23.22321...\r\n" );
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document.write( "For the final answer, you should round this decimal number to the closest lesser integer, which is 23.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Honestly, from your description, I am not sure, which of the two possible numbers, 23 or 24,
\n" ); document.write( "do you really want, but you can make your selection on your own.\r
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\n" ); document.write( "\n" ); document.write( "In any case, the correct solution is in front of you.\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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