4. (5 marks) Lucy studied public health policy and was interested in understanding how citizens of City H had been reacting to the government's suggestion to receive a vaccine booster. In particular she would like to study N (t). the number of citizens receiving the vaccine booster on the t-th day after the government announced the suggestion. Based on data collected, Lucy modelled N (t) as N : 200st\"2 + 3:2 450: + 30000 (1) for O S t S 235 with i measured in days. For example, N = 30200 when t = 0 under this model. This meant that 30200 people received the vaccine booster on the Oth day (is. the same day) of the government's announcement. Note that, for simplicity, Lucy had assumed both N and 1! take on continuous values rather than being discrete. (a) While N (t) informs Lucy of the number of citizens receiving the vaccine booster on a certain day, it would be important to know the cumulative number of citizens receiving the booster. According to Lucy's model, what is the cumulative number of citizens who received the vaccine booster between t = 0 and t = 100? Give your answer correct to 5 signicant gures. (b) According to Lucy's model, what would be the rate of change of N when t = 2? Give your answer correct to 5 signicant gures