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Advanced Math / Nonlinear functions Difficulty: Medium

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?

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Explanation

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’s given that there are $44,000$ bacteria at the start of the observation. Therefore, $a equals 44,000$ . It’s also given that the number of bacteria doubles, or increases by a factor of $2$ , every day. Therefore, $b equals 2$ . Substituting $44,000$ for $a$ and $2$ for $b$ in the equation $y = a {(b)}^{t}$ yields $y equals 44,000 left parenthesis 2 right parenthesis Superscript t$ .

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.