Explanation Given information: The linear function changes with the constant rate of change and exponential functions are noted to change with the relative rate of change. Consider the statement that the linear function changes with the constant rate of change and exponential functions are noted to change with the relative rate of change. Begin with the definition of the relative rate of change. The relative rate of change of a function f ( x ) is given by the ratio of the first derivative f ' ( x ) of the function to the function f ( x ) . Mathematically, Relative Rate of Change = f ′ ( x ) f ( x ) Consider a linear function h ( x ) = α x + β . Determine the first derivate of g ( x ) . g ′ ( x ) = α Thus, the linear function changes with the constant rate of change. Now consider the exponential function g ( x ) = e α x

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 2, Problem 55SYU

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If the statement, “The linear function changes with the constant rate of change and exponential functions are noted to change with the relative rate of change.” is true or false.

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Chapter 2, Problem 54SYU

Chapter 2, Problem 1FOT

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Chapter 2 Solutions

APPLIED CALCULUS (WILEY PLUS)

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If the statement, “The linear function changes with the constant rate of change and exponential functions are noted to change with the relative rate of change.” is true or false.

Solution Summary: The author explains that the linear function changes with the constant rate of change and exponential functions are noted to change with relative rates.

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If the statement, “The linear function changes with the constant rate of change and exponential functions are noted to change with the relative rate of change.” is true or false.

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