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A sample of single celled marine algae from the Giant Stairs site provided an estimate of 100,000 cells on the initial sampling date. Ten days later, the population size was estimated to be 600,000 cells. Calculate the per capita rate of increase (r) for the population.

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sqdancefan

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Answer:

  r ≈ 19.6% per day

Step-by-step explanation:

The growth of the population can be modeled by ...

  P = P0 × (1 +r)^t

where P0 is the initial population, r is the growth rate (per day), and t is the number of days. Using the given numbers, we can find r to be ...

  600,000 = 100,000 × (1 +r)^10

  6^(1/10) = 1 +r

  r = 6^0.1 -1 ≈ 0.196231

The growth rate per day is about 19.6%.

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