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Lecture

# 157IQsol7.pdf

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School
Department
Mathematics
Course
MATH 157
Professor
Stephen Choi
Semester
Fall

Description
MATH 157 - D100A SSIGNMENT #7 Due date: Wednesday Mar 14, 2012 Instructor Questions accompanying paper Assignment # 7 Solution Directions: Print double sided, write your solutions to both questions directly on this page, place immediately after cover page and staple together! Marks: An answer without a detailed solution process will be awarded zero marks! Q1: The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by p = 18 ▯ 3e▯2t ▯ 6e▯t=3. a) What is the price of the commodity at t = 0? Solution: ▯2▯0 ▯0=3 p(0) = 18 ▯ 3e ▯ 6e = 18 ▯ 3 ▯ 6 = 9 (in dollars) b) How fast is the price of the commodity changing at t = 0? Solution: ▯ ▯ 0 ▯2t 1 ▯ 3 p (t) = ▯3(▯2)e ▯ 6 ▯ 3 e ▯2t ▯t=3 = 6e + 2e : So 0 ▯2▯0 ▯0=3 p (0) = 6e + 2e = 6 + 2 = 8: c) Find the equilibrium price of the commodity? (Hint: It is given by lit!1.) Solution: Since lim e ▯at = 0 for any a > 0, so t!1
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