Suppose that in 1620, a ship with 100 young Ukrainian pilgrims arrived at the shores of New England to establish a new settlement. Amongst them, there was an entrepreneurial carpenter who also happen to be well versed in Differential Equations. While crafting his business plan, clever carpenter assumed that the population of his newly established town will grow at the annual rate of approximately 3.8%. a) Model this growth with a differential equation (start from dP/dt = KP and derive the solution) (8pt) b) Assuming that the people of that town only used wooden chairs for sitting (and one person needs only one chair to sit), please help the carpenter verify his calculations and determine how many chairs will the town need in the year 1640? What about 1700? What about 2021? (6pt) c) Please also help the Mayor to determine at which rate population of that town will be changing in the year 1645? This information will really help the city council to determine, how many baby cribs town will need that year! (6pt)