What fraction of a radioactive sample decay after three half lives?

Radioactive decay is a statisticle process i.e., we cannot precisely predict the timing of a particular radioactivity of a particular nucleus . The nucleus can disintegrate immediately or it may take infinite time . Simply the probability of the number of nuclei being disintegrated at any instant can be predicted . the rate at which a particular decay process in a radioactive sample is directly proportional to the number of radioactive nuclei present and thus obeys first order kinetics . the factor dN/N expresses the fraction of nuclei decayed in time dt. t_(1//2) is the time in which half of the atoms are decayed and average life is the time for the nucleus to survive before decay . 75 atoms of a radioactive species are decayed in 2 half lives (t_(1//2) = 1 hr ) if 100 atoms are taken initially . Number of atoms decayed if 200 atoms are taken in 2 hr are :

Consider a radioactive nuclide which follow decay rate given by A (t) = A_(0)2^(-(l//t_(0))), where A (f) is the fraction of radioactive material remaining after time t from the initial A_(0) at zero time. Let A_(1) be the fraction of orginal activity which remains after 120 hours. likewise A_(2) is the fraction of 200 hours. If (A_(1))/(A_(2))= 1.6, then the half-life (t_(0)) will be

A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes. (a) What is the decay constant of the sample ? (b) What is its half-life?