1. A friend of yours recently graduated and must start paying for their college loan of $50,000. The annual interest rate is 5% and is compounded continuously. Your friend plans to pay $200 monthly. Let P(t) denote the amount of money left to pay and assume that the loan is compounded continuously. a) (3pts) Write down a differential equation for this scenario and solve the equation. How long will it take your friend to pay off the loan in this case and how much will they have paid by then? Note: We did a similar problem in class many weeks ago (Look at Modeling Note 4 and Homework 7). b) (3pts) 3 years after graduation, your friend is promoted to a manager position and thus gets paid more. The friend now pays $500 monthly to the college loan. How long will it take your friend to pay off the loan in this case and how much will they have paid by then? c) (3pts) 4 years after being promoted, your friend now has kids and buys a house. With kids and the house mortgage, your friend cannot afford $500 monthly payment anymore. The friend now pays $350 monthly to the college loan. How long will it take your friend to pay off the loan in this case and how much will they have paid by then? d) (Ipt) What do you learn from these results? Note: This is an open question; there are more than one correct answer. 2. (EXTRA CREDIT, +1 pts, DUE 12/04 NO GRACE PERIOD) Can F(s)=s+2 be a Laplace transform of a piecewise continuous and of exponential order function? Justify your