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Thread: College algebra word problem

  1. #1
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    College algebra word problem

    Thorium-228 has a half life of 1.912 years. In how many years will 75% of a sample decompose? Round answer to nearest thousandth. Show all work.
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    Re: College algebra word problem

    We don't do homework; show how far you got and we'll help...
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  3. #3
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    Re: College algebra word problem

    All I got so far is: 1/2 n =1/4
    n ln (1/2)= ln 1/4
    n=2
    2x 1.912=3.824
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: College algebra word problem

    I would let $\displaystyle A(t)$ be the amount of Thorium-228 present at time $\displaystyle t$. From the information given regarding the half-life, we may then write:

    $\displaystyle A(t)=A_0\left(\frac{1}{2}\right)^{\Large \frac{t}{1.912}}$

    Now, set the equal to a quarter of the initial sample:

    $\displaystyle A_0\left(\frac{1}{2}\right)^{\Large \frac{t}{1.912}}=\frac{1}{4}A_0$

    Divide through by $\displaystyle A_0$:

    $\displaystyle \left(\frac{1}{2}\right)^{\Large \frac{t}{1.912}}= \frac{1}{4}=\left(\frac{1}{2}\right)^2$

    Equate exponents:

    $\displaystyle \frac{t}{1.912}=2$

    $\displaystyle t=3.824\quad\checkmark$
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