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Homework Help: Simple exponent variable

  1. Jan 18, 2010 #1
    1. The problem statement, all variables
    a sample polonium-218 decays at A(t)=100(.5)^t/3.1
    determine how many minutes it will take to decay to 30%

    2. Relevant equations
    log(a)/log(b)


    3. The attempt at a solution

    .3=100(.5)^t/3.1
    .3/100=.5^t/3.1
     
  2. jcsd
  3. Jan 18, 2010 #2
    I realize this is simple but I am forgetting and don't have my textbook
     
  4. Jan 18, 2010 #3

    Mentallic

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    You've already done this:

    [tex]0.3=\frac{100(0.5)^t}{3.1}[/tex]

    [tex]\frac{0.3}{100}=\frac{(0.5)^t}{3.1}[/tex]

    So why don't you follow the same kind of procedure and multiply by 3.1 :smile:

    and remember the log laws that if [tex]a^x=b[/tex] then [tex]log_ab=x[/tex]

    and finally... (which you tried to show in the relevant equations but the equation was surprisingly cut short) ... [tex]log_cb=\frac{log_ab}{log_ac}[/tex]
     
  5. Jan 18, 2010 #4
    The exponent is divided by 3.1, not the equation
     
  6. Jan 18, 2010 #5

    Char. Limit

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    In that case, just use the log-exp switchy thingy immediately.
     
  7. Jan 18, 2010 #6

    Dick

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    Fine. But you can still take the log of both sides and get a linear equation in t, can't you?
     
  8. Jan 19, 2010 #7

    Mentallic

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    The log laws still apply.
     
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