radioactive/exponential decay

Hi!

I understand the concept of radioactive decay when you have only one element.

$\displaystyle

\frac{dy}{dt}=-k\times y

$

But what happens when one element decays into a second element and the second decays into a third. What is the quantity of not decayed material of the second element? And what if you have a longer chain? For example:

Element A has a half-life $\displaystyle T_1=2 s.$

Element B has a half-life $\displaystyle T_2=5 s.$

Element C is stable.

A decays to B which decays to C.

A(t), B(t), C(t) - is the quantity of A, B, C at time t

$\displaystyle A(t)=2^{-t/2}\times A(0)$

B(t)=?

C(t)=?