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Math Help - commercial math help..plz

  1. #1
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    Question commercial math help..plz

    given that carbon decays at a constant rate in a such a way that it reduces to 20% in 1562 years. the age of the wooden piece in which the carbon is only 4% of the original

    given that carbon-14 decays at a constant rate in such a way that it reduced to 25% in 1244 years.. find the age of the tree in which the carbon is only 6.25% of the original

    the simple interest and compound interest on a certain sum for 2 years are rs. 800 and rs. 880 respectively. the rate of interest (in % p.a.) on both the sums is the same. if the interest on the sum lent at compound interest is compounded annually, find the rate of interest (in % p.a.)

    A man wants to divide rs.145000 between his son and daughter who are 12 years and 14 years respectively, in such a way that the sum invested at the rate of 25/3% per annum compounded annually will give the same amount to each, when they attain 16 years. how should he divide the sum

    A man invested one-fifth of the capital at 5% p.a., one - sixth of the capital at 6% p.a., and the rest at 10% p.a., simple interest. If the annual interest received on his investment is rs.150, then find the capital.

    How much % greater than the cost price should a shopkeeper mark his goods so that after allowing a discount of 22% on the marked price, he gains 17%.

    thanks a lot.
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  2. #2
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    Re: commercial math help..plz

    Let 100 be the cost price and 100 + x be the market price. The selling price is (100 + x)0.78 . The profit will be (100+x)0.78 - 100 = 117. Solve for x.
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  3. #3
    MHF Contributor MarkFL's Avatar
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    Re: commercial math help..plz

    For the first two, we may use exponential decay:

    A(t)=A_0e^{-kt} where 0<k

    We are being asked in these problems to find an age, which means we should solve for t:

    \frac{A(t)}{A_0}=e^{-kt}

    -kt=\ln\left(\frac{A(t)}{A_0} \right)

    t=\frac{1}{k}\cdot\ln\left(\frac{A_0}{A(t)} \right)

    Now, suppose we know:

    A(t_1)=a \cdotA_0 where 0<a\le1.

    Hence, we may state:

    A_0e^{-kt_1}=a\cdotA_0

    e^{-kt_1}=a

    -kt_1=\ln(a)

    k=-\frac{\ln(a)}{t_1} and so:

    t=\frac{t_1}{\ln(a)}\cdot\ln\left(\frac{A(t)}{A_0} \right)

    In both problems, we may take A_0=1 hence:

    t=\frac{t_1}{\ln(a)}\cdot\ln(A(t))

    Now, can you identify the parameters for the two problems?
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