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23 September, 14:22

A 30 gram sample of a substance that's used to sterilize surgical instruments has a k-value of 0.1253. Find the substance's half life in days, round to the nearest tenth.

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  1. 23 September, 14:38
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    Initial Amount: Ao=30 grams

    k=0.1253

    Amount after t days: A (t)

    A (t) = Ao*e^ (-kt)

    Half-life is the time t=T when A (t) = Ao/2:

    Ao/2=Ao*e^ (-0.1253T)

    Dividing both side by Ao:

    1/2=e^ (-0.1253T)

    Applying natural logarithm (ln) to both sides of the equation:

    ln (1/2) = ln[e^ (-0.1253T) ]

    ln1-ln2=-0.1253T*lne

    0-ln2=-0.1253T*1

    -ln2=-0.1253T

    Dividing both sides of the equation by - 0.1253:

    -ln2 / (-0.1253) = T

    T=ln2/0.1253

    T=0.693147181/0.1253

    T=5.531900882

    T=5.5 days

    The substance's half life is 5.5 days.
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