\f46. I'inllian learning model. The Hulljan learning model asserts that the probability p of mastering a task after t learning trials is approximated by an = 1a cit where i: is a constant that depends on the task to be learned. Suppose that a new dance is taught to an aerobics class. For this particular dance, the constant h = [1.28. a] 'What is the probability of mastering the dances steps in I trial? 2 trials? 5 trials? 11 trials? 15 trials? 20 trials? h] Find the rate of change, p'{t}. 2.. Radioactive decay. Carbonsll has a decay rate of llgT'l per year. The rate of change of an amount N of carbon-14- is given by {IN I = D.DUDIZDQTN, where t is the number of years since the decay began. a) Let ND represent the amount of carbonll' present at t = t}. Find the exponential function that models the situation. b) Suppose EDD g of carbonill' is present at t = D. How much will remain after E' yr? c) After how many years will half of the 20D g of carbon' 14 remain? El 4' 4. Chemistry. Substance A decomposes at a rate proportional to the amount of A present. :1} Write an equation relating A to the amount left of an initial amount Ag after time t. b) It is found that E g of A will reduce to 4 g in 3 hr. After how long will there be only 1 g left