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donnie1999

  • one year ago

Situation: An archaeologist in turkey discovers a spear head that contains 32% of its original amount of c-14. N= Noe^-kt No= initial amount of C-14 at time t t= time, in years k= 0.0001 Find the age of the spear head to the nearest year.

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  1. donnie1999
    • one year ago
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    @crissyyyxoxo

  2. donnie1999
    • one year ago
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    @aloud

  3. anonymous
    • one year ago
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    @phi

  4. phi
    • one year ago
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    start with \[ N= N_0e^{-kt} \] N is how much you have now, N0 is how much you started with. if we divide both sides by N0, you have \[ \frac{N}{N_0} = e^{-kt} \] N/N0 is the fraction we now have left. They tell us this is 32%, which means 32/100 or 0.32 also, they tell us k= 0.0001 put those numbers into the equation \[ 0.32= e^{-0.0001\cdot t} \]

  5. phi
    • one year ago
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    I would "take the natural log" of both sides as the next step.

  6. donnie1999
    • one year ago
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    whats that?

  7. phi
    • one year ago
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    If you are doing this type of problem, they assume you know about logarithms

  8. donnie1999
    • one year ago
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    @phi I am kind of clueless to these types of questions I was hoping you could help me out a little more.

  9. phi
    • one year ago
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    natural log , written ln means "exponent of base e" for example, if you write \[ e^x \] the natural log of that \[ \ln\left(e^x\right) = x \] is the exponent

  10. phi
    • one year ago
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    you want to use that idea on your equation to "get" the exponent -0.0001*t so write ln ( e^-0.0001*t) but because it is an equation, do the same to the other side, and write ln(0.32) now simplify the right-hand side using the rule: ln( e^stuff) simplifies to stuff

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