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Emily778

  • 2 years ago

The half-life of a radioactive substance is the time it takes for half of the material to decay. Phosphorus-32 is used to study a plant's use of fertilizer. It has a half-life of 14.3 days. Write the exponential decay function for a 50-mg sample. Find the amount of phosphorus-32 remaining after 84 days.

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  1. coolsday
    • 2 years ago
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    The half-life formula is: |dw:1389736938636:dw|

  2. coolsday
    • 2 years ago
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    A is the final amount , Ao is the initial amount, h is the half-life of the substance, and t is the time

  3. coolsday
    • 2 years ago
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    just plug the variables into the formula to solve for A.

  4. Emily778
    • 2 years ago
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    how do I do the rest?

  5. coolsday
    • 2 years ago
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    Ao is 50 mg, h is 14.3, t is 84 plug it into the formula and solve for A

  6. Emily778
    • 2 years ago
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    wouldn't the answer be 146.85?

  7. Emily778
    • 2 years ago
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    @coolsday

  8. Emily778
    • 2 years ago
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    by plugging those in?

  9. dape
    • 2 years ago
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    So the half-life formula can also be written as \(2^{-\lambda t}\), where \(\lambda\) is the 'decay constant', or just \(1/h\), where h is half life. So the exponent is \(84/14.3\approx5.874\), which says that the sample will have time to halve in size about 5.9 times in the 84 days (this is an easy way to remember the formula). Putting this in, we have that \(2^{-84/14.3}\approx1.7\%\). So about 1.7% of the sample will remain. Starting with 50 mg this means that about \(50\times1.7\%=0.85\) mg of the sample will remain.

  10. dape
    • 2 years ago
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    Oh, and the 'exponential decay function' we just get by putting all this together, so \[P(t)=50\times2^{-t/14.3}\] Where t is time in days.

  11. Emily778
    • 2 years ago
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    So that's the answer?

  12. Emily778
    • 2 years ago
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    @dape

  13. Emily778
    • 2 years ago
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    hellloooo?

  14. coolsday
    • 2 years ago
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    0.85 mg will remain after 84 days if you use the formula.

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