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Advanced Math / Nonlinear functions Difficulty: Easy

At the time of posting a video, a social media channel had $53$ $53$ subscribers. Each day for five days after the video was posted, the number of subscribers doubled from the number the previous day. Which equation gives the total number of subscribers, $n$ $n$ , to the channel $d$ $d$ days after the video was posted?

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Explanation

Choice B is correct. It's given that each day for five days after a social media channel posted a video, the number of subscribers doubled from the number the previous day. Since the number of subscribers doubled each day, the relationship between $n$ $n$ and $d$ $d$ can be represented by an exponential equation of the form $n = a b^{d}$ $n = a b^{d}$ , where $a$ $a$ is the number of subscribers at the time of posting the video and the number of subscribers to the channel increases by a factor of $b$ $b$ each day. It's given that at the time of posting the video, the channel had $53$ $53$ subscribers. Therefore, $a = 53$ $a equals 53$ . It's also given that the number of subscribers doubled, or increased by a factor of $2$ $2$ , from the number the previous day. Therefore, $b = 2$ $b equals 2$ . Substituting $53$ $53$ for $a$ $a$ and $2$ $2$ for $b$ $b$ in the equation $n = a b^{d}$ $n = a b^{d}$ yields $n = 53 {(2)}^{d}$ $n equals 53 left parenthesis 2 right parenthesis Superscript d$ .

Choice A is incorrect. This equation gives the total number of subscribers to a channel for which the initial number of subscribers was $1$ $1$ and the number increased each day by $53$ $53$ times the number from the previous day.

Choice C is incorrect. This equation gives the total number of subscribers to a channel for which the number of subscribers each day was half the number from the previous day, rather than double the number.

Choice D is incorrect and may result from conceptual errors.