The number of bacteria in a liquid medium doubles every day. There are 44,000 bacteria in the liquid medium at

Question

The number of bacteria in a liquid medium doubles every day. There are 44,000 bacteria in the liquid medium at the start of an observation. Which represents the number of bacteria, y , in the liquid medium t days after the start of the observation?

Accepted Answer

Choice D is correct. Since the number of bacteria doubles every day, the relationship between t and y can be represented by an exponential equation of the form y = a b t , where a is the number of bacteria at the start of the observation and the number of bacteria increases by a factor of b every day. It&rsquo;s given that there are 44,000 bacteria at the start of the observation. Therefore, a = 44,000 . It&rsquo;s also given that the number of bacteria doubles, or increases by a factor of 2 , every day. Therefore, b = 2 . Substituting 44,000 for a and 2 for b in the equation y = a b t yields y = 44,000 2 t . 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. This equation represents a situation where the number of bacteria is decreasing by half, not doubling, every day.

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