The last few years of being a student through the COVID pandemic has been tough, and so after passing all your exams you decide you deserve a graduation present, an overseas holiday! Unfortunately you can't afford this, but you definitely deserve it, so take out 'Limble' medium loan for $11,000. The interest rate is 1% per week, and Limble expect that you pay them $245 each week until you have paid them what you owe. (i) Letting an denote the amount owed after n weeks, carefully explain why an+1 = 1.01a, - 245. (ii) Determine the equilibrium value for the recurrence relation, and interpret its meaning. Is the equilibrium value stable or unstable? (iii) What is an appropriate value for the initial condition for your model? (iv) Calculate the amount owing after 2 weeks. Show all working, but do not formally solve the difference equation. (v) Explain why the model only approximates the real world. (vi) Solve the recurrence relation, and determine how long it takes to pay off the the loan.