Chapter 3.3, Problem 6E

(a)

To determine

The ratio $\frac{A\left(t\right)}{K\left(t\right)}$ for the differential equation $\frac{dK}{dt}=-\left({\lambda }_1+{\lambda }_2\right)K$ where $K\left(0\right)=K_o$ and the differential equation $\frac{dA}{dt}={\lambda }_{2}K$ where $A\left(0\right)=0$.

(b)

To determine

To show: The identity $t=\frac{1}{{\lambda }_1+{\lambda }_2}\ln \left(1+\frac{{\lambda }_1+{\lambda }_2}{{\lambda }_2}\frac{A\left(t\right)}{K\left(t\right)}\right)$.

(c)

To determine

The approximate age of the rock.