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.
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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)
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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.
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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?