MATH 172 Exam 2, Spring 2004 - Prof. M. Miller, Exams of Mathematics

Download MATH 172 Exam 2, Spring 2004 - Prof. M. Miller and more Exams Mathematics in PDF only on Docsity! MATH 172 Spring, 2004 Exam #2 Name: There are 100 points. For full credit you must show your work. You may use a calculator, but this does not exempt you from explaining your answers by giving results of computations or sketches of graphs, etc. 1. (36 points) For each model equation, and initial condition, first give the solution equation. Then answer the other questions. a. Model equation un = (1.07)un−1 with initial condition u0 = 350 ; then u5 = . b. Model equation P ′(t) = 0.07P (t) with initial contion P (0) = 350 ; then P (5) = . The population is double the initial population when t = . c. Model equation zn = zn−1 + (3/2) with initial condition z0 = 9 . d. Model equation vn = 0.96vn−1 + 5 with v0 = 200 . Does the equilibrium appear to be stable (yes or no)? . Briefly explain. e. In (d) compute the ratio vn − E vn−1 − E and explain its significance by saying how rapidly vn goes towards or away from the equilibrium. f. (7 bonus points) Model equation P ′ = −0.04P + 5 with P (0) = 200 . 2. (10 points) Verify that Q(x) = 2x2 + cx + d , where c and d are constants, satisfies the model equation Q′′(x) = 4 . Compute the values of c and d so that Q(0) = 5 and Q′(0) = 3 . 3. (7 points) Convert r = 2 , θ = 5π/6 (radians) to (x, y) coordinates. Also give the equivalent measure of θ = 5π/6 in degrees. 4. (10 points) The period of sin(3x) is x = . Find A and B so that A cos(Bx) has an amplitude of 5 and a period of 4.