Explanation Given: Function f ( t ) = 4.5 t − 4 . Formula Used: Relative rate of change of f ( t ) is given as d d t ln f ( t ) . Calculation: Function is given as f ( t ) = 4.5 t − 4 . Taking natural logarithm on both sides, we have ln f ( t ) = ln ( 4.5 t − 4 ) ln f ( t ) = ln ( 4.5 ) + ln ( t − 4 ) . Thus, relative rate of change is calculated as d d t ln f ( t ) = d d t ( ln ( 4.5 ) + ln ( t − 4 ) ) d d t ln f ( t ) = d d t ( ln ( 4.5 ) ) + d d t ( ln ( t − 4 ) ) ------ Eq(1) Solving d d t ( ln ( 4.5 ) ) . d d t ( ln ( 4.5 ) ) = 0 Solving d d t ( ln ( t − 4 ) ) . Applying chain rule of derivative. Let u = t − 4 and f = ln u . d d t ( ln ( t − 4 ) ) = d f d u . d u d t d d t ( ln ( t − 4 ) ) = d d u ( ln u )

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Chapter 3.3, Problem 32P

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To findthe relative rate of change of f(t) using the formula ddtlnf(t).

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Chapter 3.3, Problem 31P

Chapter 3.3, Problem 33P

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To findthe relative rate of change of f ( t ) using the formula d d t ln f ( t ) .

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To findthe relative rate of change of f(t) using the formula ddtlnf(t).

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Chapter 3 Solutions