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MATH 1100: QUANTITATIVE ANALYSIS TEST #1 (VERSION A) Name: This test has 4 pages and 4 problems. No calculators are allowed. You are permitted only a pencil or pen. Work out everything as far as you can before making decimal approximations. The equation of continuously compounded interest is S = P ert , where P is the principal, r the nominal rate and S the value of the investment after t years. 1. By calculating the reduced form, find all solutions to x + 2y − z = 3 3x + y = 4 2x − y + z = 2. Date: September 3, 2001. 1 2 MATH 1100: QUANTITATIVE ANALYSIS 2. Using matrix inverses, solve: 4x − y = 1 x + 2y = 2 TEST #1 (VERSION A) MATH 1100: QUANTITATIVE ANALYSIS TEST #1 (VERSION A) 3 3. Suppose that $1000 is invested at 10% nominal interest rate, compounded continuously. (a) Write an equation describing the value of the investment after t years since the principal was invested. (b) Approximate the value of the investment after 30 years, using the approximation e ∼ 3. (c) How many years does it take for the investment to double in value? Hint: use the approximation ln(2) ∼ 0.7. 4 MATH 1100: QUANTITATIVE ANALYSIS TEST #1 (VERSION A) 4. Your company makes two products, A’s and B’s. The A’s require 2 hours of work each to make, while the B’s require 4. You have 800 work hours available each day to make them. But you can only transport a total of 300 products (A’s and B’s together) in a day. A’s sell for $30, B’s for $40. Suppose you will always sell as many as you make. How many of each should you make to maximize sales revenue?