12. The cumulative exponential probability distribution describes the probability P(t) that a particular radioactive atom will decay within t minutes. It is given by P(t) = 1 -e-At where A is a positive constant. The domain is restricted to t 2 0. (a) [2 marks] Find the horizontal asymptote of P(t). Answer: (b) [2 marks] Find the intercepts of P(t). Answer: Student number: 17(c) [3 marks] Draw a large sketch of the graph of P(t) on the axes below, using the information determined in the previous parts of this question. 21 (d) [3 marks] The haUltfe of a radioactive isotope is the time taken for a sample of the isotope to decay to half of its original mass. It is equal to the time by which the probability of decay of an individual atom is %. What is the half-life of the isotope whose atoms have the cumulative exponential probability distribution described above? Answer: Student numb er: 18