3. a) the number initially is 20 000, the number decrease by 20% each year. Find i) the value of N0 ii) the value of k

1 In the initial period of its life a particular species of tree grows in the manner described by the rule d = do 10" where d is the diameter of the tree in centimetres, t years after the beginning of this period. The diameter after 1 year is 52 cm and after 3 years, 80 cm. Calculate the values of the constants do and m." di t 1 2 2 The number of bacteria in a certain culture at time, t weeks, is given by the rule N = Noek If when t = 2, N = 101 and when t = 4, N = 203 calculate the values of No and k. 13/ The number of people, N, who have a particular disease at time t years is given by N = Noek a If the number initially is 20 000 and the number decreases by 20% each year, find: i the value of No ii the value of k b How long does it take for 5000 people to be infected? 4 Polonium-210 is a radioactive substance. The decay of polonium-210 is described by the formula M = Moe k, where M is the mass in grams of polonium-210 left after t days, and Mo and & are constants. At time t = 0, M = 10 g and at t = 140, M = 5 g. a Find the values of Mo and k. b What will be the mass of the polonium-210 after 70 days? c After how many days is the mass remaining 2 g