ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: /0 on March 27, 2008, 09:36:28 am
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A patient has an infection that, if it exceeds a certain level, will kill him. He is given a drug that will inhibit the spread of the infection. The drug acts in such a way that the level of infection only increases by 65% of the previous day's level. On the first day, the level of the infection is measured at 450.The critical level of infection is 1280. Will the infection kill him?
Am I missing something with this question? The way I'm looking at it, it won't even require calculation, because the measure is always increasing, but that seems too simple.
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Nevermind, stupid mistake by me
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Of course its going to kill him. u sure u copied out the question right? or is there maybe more to the question, like after how many days will he die?
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pfftt, that problem isn't even realistic :P
But anyway, I think you're asked to find the limit of a convergent geometric series. Use the formula
S¥= a/(1-r) where ‘a’ is the first term of the series, and ‘r’ is the common ratio. So in this problem, ‘a’ is 450 (the initial level of infection). ‘r’ is 0.65.
Sub these values into the equation:
S¥= 450/(1-0.65)
= 450/0.35
= 1285.71
Therefore, the maximum level of infection is 1285.71. This exceeds the critical level of infection of 1280, and so the patient would die.
Hope that made sense and hope it's actually correct
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woops, the formula didn't copy properly from microsoft word
but yeah
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Yeah thanks, so the patient does die.
It's amazing how fast the number of days rises as you approach 1285.71.... though. Even when you reach the digit in the hundredths, the number of days is only rising by about 3 or 4. Add a few more digits on, and the rise becomes very fast :D