Explanation The rate of change of income is f ( t ) = 810 e k t where t denotes time in years. It is given that, at the end of first year the rate is $797.94. So, f ( 1 ) = 797.94 Substitute t = 1 to find the value of k . f ( 1 ) = 810 e k ( 1 ) 797.94 = 810 e k 810 e k = 797.94 810 810 e k = 797.94 810 e k = 0.98511 Take natural logarithmic on both sides, ln e k = ln ( 0.98511 ) k = − 0.015 Now substitute k = − 0.015 in f ( t ) = 810 e k t and obtain f ( t ) = 810 e ( − 0

Finite Mathematics and Calculus with Applications

1st Edition

ISBN: 9781323188361

Author: Margaret Lial

Publisher: Pearson Education

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Chapter 16.3, Problem 1YT

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To find: The total income produced by a machine during the first 2 years when the initial income rate is $810/year and the income rate at the end of the first year is $797.94/year.

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Chapter 16.2, Problem 45E

Chapter 16.3, Problem 2YT

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Finite Mathematics and Calculus with Applications

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The total income produced by a machine during the first 2 years when the initial income rate is $810/year and the income rate at the end of the first year is $797.94/year.

Solution Summary: The author explains that the rate of change of income is f(t)=810ekt, where t denotes time in years.

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To find: The total income produced by a machine during the first 2 years when the initial income rate is $810/year and the income rate at the end of the first year is $797.94/year.

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Chapter 16 Solutions