Explanation Given information: The bactericide introduced when N ( t ) after a certain time t min is, N ( t ) = 10 , 000 1 + t 2 + 2000 (1) The values of culture time is 1 min and 2 min . Formula used : The quotient rule of differentiation is, f ′ ( x ) = d d x [ f ( x ) g ( x ) ] = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) [ g ( x ) ] 2 The above formula is defined when the denominator g ( x ) ≠ 0 . Calculation: Section1: Use the quotient rule of differentiation for the equation (1) to get the rate of change of number of bacteria with t that is N ′ ( t ) . N ′ ( t ) = d d t ( 10 , 000 1 + t 2 ) + d d x ( 2000 ) = ( 1 + t 2 ) ⋅ d d t ( 10 , 000 ) − ( 10 , 000 ) ⋅ d d t ( 1 + t 2 ) ( 1 + t 2 ) 2 + 0 = ( 1 + t 2 ) ⋅ ( 0 ) − ( 10 , 000 ) ⋅ ( 2 t ) ( 1 + t 2 ) 2 = − 20 , 000 t ( 1 + t 2 ) 2 ( Apply distributive property ) (2) Substitute 1 for t in the equation (2) to get the value of N ′ ( 1 )

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ISBN: 9781337825597

Author: Tan

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Differential Equations

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Chapter 3.2, Problem 55E

To determine

To find: The rate of change of number of bacteria introduced in the culture 1 min , 2 min and the population of bacteria introduced in the culture 1 min and 2 min .

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Chapter 3.2, Problem 54E

Chapter 3.2, Problem 56E

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Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The rate of change of number of bacteria introduced in the culture 1 min , 2 min and the population of bacteria introduced in the culture 1 min and 2 min .

Solution Summary: The author explains the rate of change of number of bacteria introduced in the culture and the quotient rule of differentiation.

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To find: The rate of change of number of bacteria introduced in the culture 1 min , 2 min and the population of bacteria introduced in the culture 1 min and 2 min .

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