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Homework Help: Logarithms disinfectant spray problem

  1. Dec 8, 2007 #1
    A new disinfectant spray is expected to kill 50% of the known germs in a room, but for health reasons it can only be used once a day. Between spraying, the germs increase by 25%. How many consecutive days of spraying are required to reduce the germs in the room to 10% of the original amount?

    Relevant equations:

    0.10Po=Po(0.50)^d + 0.25Po(0.50)^d
    0.10=0.50^d + 0.25(0.50)^d

    Can someone please tell me what I'm doing wrong? The answer is supposed to be 5 days.
  2. jcsd
  3. Dec 8, 2007 #2
    what do the variables of your relevant equation pertain to?
  4. Dec 8, 2007 #3
    A is the final amount. Ao is the initial amount. i is the increase or decrease. and n is the number of periods.
  5. Dec 8, 2007 #4
    i'm unable to follow your problem but when we solve for n, which i assume is the number of days


    divide by A initial and then take the log of both sides and then solve for n
  6. Dec 8, 2007 #5
    yea, i tried doing that. but the answer didn't come out right.
  7. Dec 8, 2007 #6


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    Homework Helper

    If A is the number of germs then after spraying A->0.5*A. After waiting a day that number increases by 25%. So that's multiplication by 1.25. Put the two together and from one day to the next A->0.5*A*1.25=0.625*A. So that's 0.1=(0.625)^n.
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