The increase in the number of viruses in four time step.

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Chapter 1, Problem 9QP

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The increase in the number of viruses in four time step.

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A certain strain of bacteria will divide itself from 1 to 2 every to [minute]. As a result, its population can be modeled as N (t) = No2. ---(eq 1) N(t) is the population at time t, NO is the population at the beginning = 100, t = time you wait [minute]. You prepare 6 dishes. Each dish contains 100 living bacteria at the beginning. Then you wait for 20 mins, freeze the first dish to stop the bacteria in the dish from growing. Then wait for another 20 mins, freeze the second dish (i.e. the total growth time for the second dish is 40 min). Proceed to the next dish in the similar process until all 6 dishes are done. After counting all the dish, you collect the data between time and population as follow: t(min) N(t) 20 132 220 40 60 311 80 369 100 622 120 836 Find to (the time for bacteria to divide itself). Answer in [min] Note: if you apply log function on both sides of eq 1 you get In (N (t)) =t. n2 + In(No). ---(eq 2)

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