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Advanced Math / Nonlinear functions Difficulty: Medium

A company has a newsletter. In January $2018$ , there were $1,300$ customers subscribed to the newsletter. For the next $24$ months after January $2018$ , the total number of customers subscribed to the newsletter each month was $7 percent sign$ greater than the total number subscribed the previous month. Which equation gives the total number of customers, $c$ , subscribed to the company's newsletter $m$ months after January $2018$ , where $m less than or equals 24$ ?

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Explanation

Choice B is correct. It's given that in January $2018$ , there were $1,300$ customers subscribed to a company's newsletter and for the next $24$ months after January $2018$ , the total number of customers subscribed to the newsletter each month was $7 percent sign$ greater than the total number subscribed the previous month. It follows that this situation can be represented by the equation $c = a {(1 + \frac{r}{100})}^{m}$ , where $c$ is the total number of customers subscribed to the company's newsletter $m$ months after January $2018$ , $a$ is the number of customers subscribed to the newsletter in January $2018$ , and the total number of customers subscribed to the newsletter each month was $r %$ greater than the total number subscribed the previous month. Substituting $1,300$ for $a$ and $7$ for $r$ in this equation yields $c = 1,300 {(1 + \frac{7}{100})}^{m}$ , or $c equals 1,300 left parenthesis 1.07 right parenthesis Superscript m$ .

Choice A is incorrect. This equation represents a situation where the total number of customers subscribed each month was $93 percent sign$ less, not $7 percent sign$ greater, than the total number subscribed the previous month.

Choice C is incorrect. This equation represents a situation where the total number of customers subscribed each month was $70 percent sign$ , not $7 percent sign$ , greater than the total number subscribed the previous month.

Choice D is incorrect. This equation represents a situation where the total number of customers subscribed each month was $600 percent sign$ , not $7 percent sign$ , greater than the total number subscribed the previous month.