Answer
$N_D=N_o(1-e^{-\lambda t})$
Work Step by Step
The number of radioactive nuclei that are left decreases exponentially.
$$N=N_oe^{-\lambda t}$$
The number that decayed is the original number minus that.
$$N_{decayed}= N_o -N$$
However, each radioactive nucleus that decays becomes a daughter nucleus, and that is the formula we seek.
$$N_{decayed}=N_D= N_o -N$$
$$N_D=N_o- N_oe^{-\lambda t} =N_o(1-e^{-\lambda t})$$
