Math 3200 - Sample Exam #2
Spring 1998 - Briggs' Section

This is a 75-minute in-class exam. You are allowed to use a page of notes and a calculator. Please show and justify all of your work clearly.

1. Assume that the consumer price index (CPI) has risen at a rate of 4% per year since 1984 when its value was set at 100.
   1. Assuming that this growth remains constant, find a function that gives theCPI for all times after 1984. Sketch a graph of this function.
   2. What is the doubling time for the CPI.
2. Which of the following pairs of functions are linearly independent? Explain.

   

3. Find the general solution of the following homogeneous ODEs.

   

4. Consider the ODE . Classify the ODE in terms of linearity and order. Transform the ODE to a simpler linear ODE, solve it, and find the general solution to the original problem.
5. Consider the ODE . Classify the ODE in terms of linearity and order. Find the general solution. Find the solution that satisfies y(1)=1.

   Answers (not complete solutions)

   1. a. . b. .

   2. A and B are linearly independent; C and D are linearly dependent.

   3. a. . b. .

   4. Linear ODE: . General solution of linear ODE: . Solution to original ODE: .

   5. .