Introduction to mat hematical modelling assignment 1 due: see l@g (2018) 2204nsc remember to attach a signed coversheet to your assignment. 1. two of the simplest population models are the exponential growth model and the logistic growth model. the differential equations for the two models are given by dn dt i. exponential growth: -=rn logistic growth dn=rn(i ) where n is the size of the population at time t, r is the growth rate and k is the carrying capacity the population data of a cell line in a petri dish is given below. time (years) n 20 40 60 80 100 200 740 1560 2000 2170 2190 (a) solve both of the given models to obtain an expression for n(t) given that n(0) (b) what is the long term beh aviour of n(t) for each of the models? no (e) determine which of the two given models best fits the dat a. make sure that you justify (d) for the model chosen in part (c), estimate values for the unknown parameters and the e) produce a graph that shows the known data points for the population as well as the your answer initial condition. make sure that youl explain why you have chosen these values. solution to the chosen model with the estimated parameter values estimated from part (d).