Explanation Given: The given equation is, 200 1 + 3 e − 0.3 t = 100 (1) Calculation: Multiply both the sides of above equation (1) by 1 + 3 e − 0.3 t . 200 1 + 3 e − 0.3 t ⋅ ( 1 + 3 e − 0.3 t ) = 100 ⋅ ( 1 + 3 e − 0.3 t ) 200 = 100 + 300 e − 0.3 t 100 = 300 e − 0.3 t [ Subtract 100 ] 100 300 = e − 0.3 t [ Divide by 300 ] Take natural logarithm of above equation. ln 100 300 = ln e − 0.3 t ln 1 3 = − 0.3 t ln e [ ∵ ln a b = b ln a ] − 1 0

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 5.2, Problem 42E

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To solve: The equation 2001+3e−0.3t=100 for t .

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Chapter 5.2, Problem 41E

Chapter 5.2, Problem 43E

Chapter 5 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

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The equation 200 1 + 3 e − 0.3 t = 100 for t .

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Chapter 5 Solutions