Explanation Given information: In an experiment, a certain type of bacteria was being added to a culture at the rate of e 0.03 t + 2 thousand bacteria per hour. The bacteria grows at a rate proportional to the size of the culture at time t , with the constant of proportionality k = 0.45 . Explanation: Let P ( t ) denote the number of bacteria in the culture at time t and it satisfies the differential equation y ' = 0.45 y + e 0.03 + 2 ⇒ y ' − 0.45 y = e 0.03 + 2 Comparing this with y ' + a ( t ) y = b ( t ) a ( t ) = − 0.45 and b ( t ) = e 0.03 + 2 Initial condition is y ( 0 ) = 10 A ( t ) = ∫ − 0.45 d t = − 0.45 t Now, using an integrating factor, y = e − A ( t ) ∫ b ( t ) e A ( t ) d t + C = e 0.45 t [ ∫ [ e 0.03 t + 2 ] e − 0

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ISBN: 9780137590896

Author: Larry J. Goldstein; David C. Lay; David I. Schneider; Nakhle H. Asmar; William Edward Tavernetti

Publisher: Pearson Education (US)

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Chapter 10.4, Problem 18E

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The formula for P(t), where P(t) satisfies y'=0.45y+e0.03+2 with the initial condition that ten thousand bacteria were present in the culture.

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Chapter 10.4, Problem 17E

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The formula for P ( t ) , where P ( t ) satisfies y ' = 0.45 y + e 0.03 + 2 with the initial condition that ten thousand bacteria were present in the culture.

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The formula for P(t), where P(t) satisfies y'=0.45y+e0.03+2 with the initial condition that ten thousand bacteria were present in the culture.

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