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# sols6 - SOLUTIONS TO HOMEWORK ASSIGNMENT#6 1 A culture of...

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Unformatted text preview: SOLUTIONS TO HOMEWORK ASSIGNMENT #6 1. A culture of bacteria is found to contain 10 4 bacteria per cm 3 at the start of an experiment. After 1 day there are 10 6 bacteria. Assume that the number of bacteria increases at a rate that is proportional to the number of bacteria present. (a) Determine the doubling time of the bacteria. (b) How many will there be after 2 days? Solution: (a) If B ( t ) is the number of bacteria at time t then B ( t ) = B (0) e kt = 10 4 e kt for some constant k. We are given B (1) = 10 6 , and thus 10 6 = 10 4 e k = ⇒ k = ln 100 . We get the doubling time τ by solving the equation 2 = e kτ for τ. Therefore τ = ln 2 k = ln 2 ln 100 ≈ . 15 days ≈ 3 . 6 hours . (b) The number will be B (2) = 10 4 e 2 k = 10 4 e 2 ln100 = 10 4 × 100 2 = 10 8 . 2. In a chemical reaction it is found that a substance is broken down at a rate proportional to the amount of substance remaining. It was observed that 10 g of the substance decreased to 8 g in 1 hr....
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sols6 - SOLUTIONS TO HOMEWORK ASSIGNMENT#6 1 A culture of...

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