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A biologist grows a culture of bacteria as part of an experiment. At the start of the experiment, there are 75 bacteria in the culture. The biologist observes that the population of bacteria dobules evert 18 minutes. Which of the following equations best models the number, n, of bacteria t hours after the start of the experiment.

a. n=75(2)^t/18
b. n=75(1+t/18)
c. n=75(2)^10t/3
d. n=75(1+(10/3)t)

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  1. a would be a perfect answer if t was in minutes. But it is in hours. There are 10/3 eighteen minutes in an hour, and the number of doubling periods is 10t/3

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    bobpursley
  2. when t = 0, n = 75 (note 2^0 = 1)
    when t = 18, n = 75 * 2^1 (note 18/18 = 1)
    when t = 36 , n = 75 * 2^2 (note 36/18 = 2 ) etc

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  3. whoops, sorry, did not notice the hours/minutes problem

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  4. the 10t/3 that bob talks about is in c

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