Bacteria are growing in a liquid growth medium. There were 300,000 cells per milliliter during an initial observation. The number of cells per milliliter doubles every 3 hours. How many cells per milliliter will there be 15 hours after the initial observation?

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Accepted Answer

Choice D is correct. Let y represent the number of cells per milliliter x hours after the initial observation. Since the number of cells per milliliter doubles every 3 hours, the relationship between x and y can be represented by an exponential equation of the form y = a(b) x/k , where a is the number of cells per milliliter during the initial observation and the number of cells per milliliter increases by a factor of b every k hours. It’s given that there were 300,000 cells per milliliter during the initial observation. Therefore, a = 300,000. It’s also given that the number of cells per milliliter doubles, or increases by a factor of 2, every 3 hours. Therefore, b = 2 and k = 3. Substituting 300,000 for a, 2 for b, and 3 for k in the equation y = a(b) x/k yields y = 300,000(2) x/3 . The number of cells per milliliter there will be 15 hours after the initial observation is the value of y in this equation when x = 15. Substituting 15 for x in the equation y = 300,000(2) x/3 yields y = 300,000(2) 15/3 , or y = 300,000(2) 5 . This is equivalent to y = 300,000(32), or y = 9,600,000. Therefore, 15 hours after the initial observation, there will be 9,600,000 cells per milliliter. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

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