Explanation Given: Initial the amount of carbon dioxide present = 0.15%. Percentage of fresh air = 0.05%. The rate of mixed in and mixed out of carbon dioxide = 2 m 3 / min . Calculation: Let y be the amount of carbon dioxide. At the initial stage carbon dioxide level is y (0) = 0 15%(180 m 3 ) at time zero. y = 0.0015 ( 180 ) = 0.27 m 3 Here 180 m 3 is the volume carbon dioxide constantly. Then the percentage of carbon dioxide is y 180 ( 100 ) at time t . The rate of change carbon dioxide with respect to time t , d y d t = 0.05 100 ( 2 ) − y 180 ( 2 ) Here y 180 ( 2 ) be the carbon dioxide flows inside. d y d t = 0.001 − y 90 d y d t = 0.09 − y 90 Multiply 100 on both sides, d y d t = 9 − 100 y 9000 Separate the variables, d y 9 − 100 y = d t 9000 Integrating on both sides, ∫ d y 9 − 100 y = ∫ d t 9000 − 1 100 ln ( 9 − 100 y ) = 1 9000 t + C (1) Substitute initial condition y ( 0 ) = 0.27 in equation (1), − 1 100 ln ( 9 − 100 ( 0.27 ) ) = 1 9000 ( 0 ) + C − 1 100 ln ( 18 ) = C Substitute C value in equation (1), − 1 100 ln ( 9 − 100 y ) = 1 9000 t − 1 100 ln ( 18 ) − ln ( 9 − 100 y ) = t 90 − ln ( 18 ) ln ( 9 − 100 y ) = − t 90 + ln ( 18 ) Take exponentials on both sides, ln ( 9 − 100 y ) = − t 90 + ln ( 18 ) 9-100 y is negative

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Chapter 9.3, Problem 46E

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To find: The function for the percentage of carbon dioxide present in the room at time t. And to find the limit of the function that we found.

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Chapter 9.3, Problem 45E

Chapter 9.3, Problem 47E

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Bundle: Single Variable Calculus: Early Transcendentals, Loose-leaf Version, 8th + Webassign Printed Access Card For Calculus, Multi-term Courses, Life Of Edition

Ch. 9.1 - Show that y=23ex+e2x is a solution of the...Ch. 9.1 - Prob. 2E Ch. 9.1 - (a) For what values of r does the function y = erx...Ch. 9.1 - (a) For what values of k does the function y = cos...Ch. 9.1 - Which of the following functions are solutions of...Ch. 9.1 - (a) Show that every member of the family of...Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

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The function for the percentage of carbon dioxide present in the room at time t . And to find the limit of the function that we found.

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To find: The function for the percentage of carbon dioxide present in the room at time t. And to find the limit of the function that we found.

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Chapter 9 Solutions