Mathematical Models

Homework Assignment #2

Due Wednesday, January 29, 11:00 am

Homework should be turned in at the BEGINNING OF CLASS. Unless otherwise specified, all problem numbers refer to Giordano, Weir and Fox, the required text for the course. You should write up solutions neatly to all problems, making sure to SHOW ALL YOUR WORK. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be your own work. At the top of your homework, please list any students you work with or any other resources you found helpful (websites, books, faculty, etc.)

Section 1.3
Problems:   1b, 1d, 1e, 2e, 2h, 2j, 3a, 3b, 3e, 4a, 4d, 6, 8*

Note: Problem #3a should have an a_n in the equation (the subscript n is missing). For problem #3 (a,b,e), please turn in your graphs and numerical output. It is recommended that you use a spread sheet or MAPLE to do this problem.

For problem #8, break the problem into three parts. First, formulate a model with the monthly payment p as a variable. Just set up the model, don't solve it. For the second part, assume p = 1500 and determine the initial amount the parents can borrow so that the mortgage is completely paid off after 30 years. For the third part (my addition), generalize your work from the previous two parts. In other words, given a monthly interest rate r, a monthly deduction p and a final time N (in months), determine the value of a_0 so that the mortage is paid off in N months. Your answer will be in terms of the constants r, p and N.

Section 1.4
Problems:   4, 6

Note: You will need a spread sheet or MAPLE to do these problems. You do not have to turn in any graphs or data for these problems unless you feel it significantly adds to your answer. Well-written paragraphs are sufficient here.