To determine The number of cubic feet x as a function of t. Explanation Fresh air is being circulating into a room whose volume is 4000 ft 3 . The boundary condition x = 12 ft 3 when t = 0 The differential equation is given as follows: d x d t = 1 − 0.25 x Solving the separation of variables in the equation d x d t = 1 − 0.25 x . d x 0.25 x − 1 = − d t Integrating the equation d x 0.25 x − 1 = − d t . ∫ d x 0.25 x − 1 = ∫ − d t 4 ln ( 0.25 x − 1 ) = − t + c Substitute the boundary condition x = 12 ft 3 when t = 0 in 4 ln ( 0.25 x − 1 ) = − t + c . 4 ln ( 0.25 × 12 − 1 ) = − 0 + c c = 4 ln 2 Substitute the value of c = 4 ln 2 in 4 ln ( 0

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Chapter 31.6, Problem 49E

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The number of cubic feet x as a function of t.

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Chapter 31.6, Problem 48E

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Ch. 31.1 - Show that is a solution of . Is it the general...Ch. 31.1 - Prob. 1E Ch. 31.1 - In Exercises 1 and 2, show that the indicated...Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 4E Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 6E Ch. 31.1 - In Exercises 7–10, show that each function y =...Ch. 31.1 - Prob. 8E Ch. 31.1 - In Exercises 7–10, show that each function y =...

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