Assessment 3. Marks: 40. Use your knowledge of difference equations, dynamical system models and solutions to dynamical systems to solve the following problems. Scan and submit your work on moodle by 30 September 2021. 1. (a) Edward wishes to buy a car and narrows his choices to a Toyota Corolla, Cavalier and Hyundai. He is able to spend at most NS 475 a month on a car payment. Each company offers him its best deal. Cost Down payment Monthly interest Corolla NS 13 990 NS 2 100 3.5% for up to 60 months Cavalier N$ 13 550 NS 2960 4.5% for up to 60 months Hyundai NS 12 400 NS 5 452 6.5% for up to 48 months (a) Write a dynamical system for each case. Using Matlab to obtain numerical solutions and a graph for each dynamical system, which car can Edward afford to buy? (10) (b) Consider the table above. Calculate the monthly payment for each type of car given. (6) NB: Write Matlab codes to test if the monthly payment you calculated for each type of car will pay off the debit at the given monthly interest within the given period. Assessment 3. Marks: 40. Use your knowledge of difference equations, dynamical system models and solutions to dynamical systems to solve the following problems. Scan and submit your work on moodle by 30 September 2021. 1. (a) Edward wishes to buy a car and narrows his choices to a Toyota Corolla, Cavalier and Hyundai. He is able to spend at most NS 475 a month on a car payment. Each company offers him its best deal. Cost Down payment Monthly interest Corolla NS 13 990 NS 2 100 3.5% for up to 60 months Cavalier N$ 13 550 NS 2960 4.5% for up to 60 months Hyundai NS 12 400 NS 5 452 6.5% for up to 48 months (a) Write a dynamical system for each case. Using Matlab to obtain numerical solutions and a graph for each dynamical system, which car can Edward afford to buy? (10) (b) Consider the table above. Calculate the monthly payment for each type of car given. (6) NB: Write Matlab codes to test if the monthly payment you calculated for each type of car will pay off the debit at the given monthly interest within the given period