Which equation represents the total number of subscribers after m months with a 7% monthly increase, starting from 1,300 subscribers in January 2018?

• A. c = 1,300(1.07)^m
• B. c = 1,300 + 0.07m
• C. c = 1,300(1.07)^(m-1)
• D. c = 1,300 - 1.07m

Answer: (C)

This models exponential growth where you start with 1,300 subscribers and each month multiply by 1.07. Since January is the first month with 1,300 subscribers, you apply the 7% increase a total of m−1 times over m months. Therefore the amount after m months is c = 1,300 × (1.07)^(m−1). For example, in January (m = 1) you have 1,300 × (1.07)^0 = 1,300; in February (m = 2) you have 1,300 × (1.07)^1 = 1,391; in March (m = 3) you have 1,300 × (1.07)^2, and so on. The other forms don’t fit because applying the growth factor every month starting from the first month would misstate January’s initial amount, a linear addition 7% per month isn’t compound growth, and subtracting the growth per month would produce a decline rather than growth.