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.(Bow)(Bow)

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.

Re: commercial math help..plz

For the first two, we may use exponential decay:

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

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

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

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

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

Now, suppose we know:

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

Hence, we may state:

$\displaystyle A_0e^{-kt_1}=a\cdotA_0$

$\displaystyle e^{-kt_1}=a$

$\displaystyle -kt_1=\ln(a)$

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

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

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

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

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