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

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.

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.