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Lv 6
One asked in Science & MathematicsMathematics · 9 years ago

Half Life-Word problem?

"Iodine-131, a radioactive substance that is effective in locating brain tumors, has a half-life of only eight days. A hospital purchased 20 grams of the substance but had to wait five days before it could be used. How much of the substance was left after five days?"

Can someone help me with this, a formula or anything, I'm stumped on it? I have the answer in the book I am using, but I need to know how to get the answer.

Update:

Thank you! I knew it was something with 5/8...

Update 2:

I'm sorry, Adrian S, but you kind of lost me just a little bit. Where did you get the "-0.08664", again?

2 Answers

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  • ?
    Lv 7
    9 years ago
    Favorite Answer

    5 days/8 days = 0.625 half lives

    fraction left after 0.625 half lives = (1/2)^0.625

    = 0.6484197773

    Amount left = 20*0.6484197773 gms

    = 12.97 gms to dp <<<

  • Adrian S
    Lv 7
    9 years ago

    Here's another way to look at the problem...

    Amt at time (t) = starting amount*e^(a*t)

    Now starting amount is 20 g and after 8 days you have 10 g.

    So plugging in and taking ln's of both sides you can find a.

    Then just use a and calculate amount remaining after 5 days.

    = 20*e^(-0.08664*5) = 12.968 g.

    Source(s): Math tutor for several years.
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