A company has a newsletter. In January 2018, there were 1{,}300 customers subscribed to the newsletter. For the next 24...

1. TRANSLATE the problem information

• Given information:
  • Initial subscribers in January 2018: 1,300
  • For 24 months after January 2018: each month has 7% more subscribers than previous month
  • Find equation for c customers m months after January 2018

• What "7% greater than previous month" means:
  If previous month had N subscribers, next month has \(\mathrm{N + 0.07N = N(1 + 0.07) = N(1.07)}\)

2. INFER the mathematical pattern

• This describes exponential growth - each month we multiply by the same factor (1.07)
• Starting value: 1,300
• Growth factor: 1.07 (since 7% increase means multiply by 1.07)

3. Apply exponential growth model

• General form: \(\mathrm{c = (initial\ value) \times (growth\ factor)^{(number\ of\ periods)}}\)
• Substitute our values: \(\mathrm{c = 1,300 \times (1.07)^m}\)
• This gives us: \(\mathrm{c = 1,300(1.07)^m}\)

Answer: B. \(\mathrm{c = 1,300(1.07)^m}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misunderstanding what "7% greater" means mathematically

Students might think:

• "7% greater" means add 7, leading to \(\mathrm{c = 1,300 + 7m}\) (linear instead of exponential)
• "7% greater" means multiply by 0.07, leading to exponential decay
• "7% greater" means multiply by 1.7, confusing 7% with 70%

Any of these translation errors would lead them away from the correct growth factor of 1.07, potentially selecting Choice C (\(\mathrm{c = 1,300(1.7)^m}\)) or Choice A (\(\mathrm{c = 1,300(0.93)^m}\)).

The Bottom Line:

The key challenge is correctly translating percentage language into mathematical operations. Students must recognize that "7% greater than" means "multiply by 1.07", not add 7 or multiply by 0.07.