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Calculus Techniques

by: Darren Schulist

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2

Calculus Techniques MATH 1100

Darren Schulist
Utah State University
GPA 3.77

Joseph Koebbe

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COURSE
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Joseph Koebbe
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Darren Schulist on Wednesday October 28, 2015. The Class Notes belongs to MATH 1100 at Utah State University taught by Joseph Koebbe in Fall. Since its upload, it has received 12 views. For similar materials see /class/230415/math-1100-utah-state-university in Mathematics (M) at Utah State University.

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Date Created: 10/28/15
Problem De nition Problem 41 Learning Theory The management of a factory has found that a worker can produce at most 30 units per day The number of units N per day produced by a new employee will increase at a rate proportional to the difference between 30 and N This is described by the differential equation IN 7 k 30 N d where t is the time in Solve this differential equation Solution Step 1 The process of separation of variables starts by moving all dependence on t to one side of the equation and all dependence on N to the other Multiplying the differential equation through by It results in IN It dt k30 Ndt or IN k30 Ndt Dividing by 30 N in trun gives IN 30 N This shows the equation is separable kdt Solution Step 2 Next we need to integrate both sides of the separated equation Integrat ing the left hand side gives dN 30 N ln 30 N Cl and fkdtktC2 Setting the integrals equal gives the equation ln 30 N CI kt Cg or ln 30 N kt C Exponentiating both sides of the equation results in 30 N e ktC 2 SC e m Solving for N gives N 30 QC 8quot This is the general solution of the original differential equation To nd a particular solution we would need an initial condition and another data point or the rate constant

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