An online community has 8{,}000 members at the start of a new outreach campaign. During the campaign, the number of...

1. TRANSLATE the problem information

• Given information:
  • Initial members: 8,000
  • Growth rate: 50% increase each month
  • Time period: 5 months
  • Find: Members after 5 months

• What "50% increase each month" means: The community size gets multiplied by 1.5 each month (since \(\mathrm{100\% + 50\% = 150\% = 1.5}\) times the original)

2. INFER the mathematical approach

• This is exponential growth, not linear growth - the community doesn't just add the same number each month
• Each month, we multiply the current size by 1.5
• We need the exponential growth formula: \(\mathrm{Final\ amount = Initial\ amount \times (growth\ factor)^{time\ periods}}\)

3. TRANSLATE into mathematical notation

• Final members = \(\mathrm{8{,}000 \times (1.5)^5}\)

4. SIMPLIFY the calculation

• Calculate \(\mathrm{(1.5)^5}\) (use calculator):
  \(\mathrm{(1.5)^5 = 7.59375}\)
• Multiply by initial amount:
  \(\mathrm{8{,}000 \times 7.59375 = 60{,}750}\) (use calculator)

Answer: D. 60,750

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students think this is linear growth instead of exponential growth.

They might calculate: \(\mathrm{50\%\ of\ 8{,}000 = 4{,}000}\), so each month we add 4,000 members. After 5 months:
\(\mathrm{8{,}000 + (5 \times 4{,}000) = 28{,}000}\).

This may lead them to select Choice A (28,000).

Second Most Common Error:

Poor SIMPLIFY execution: Students set up the problem correctly but make calculation errors with \(\mathrm{(1.5)^5}\).

For example, they might confuse \(\mathrm{(1.5)^5}\) with \(\mathrm{1.5 \times 5 = 7.5}\), giving \(\mathrm{8{,}000 \times 7.5 = 60{,}000}\), or make other computational mistakes that lead to selecting an incorrect choice like B or C.

The Bottom Line:

The key insight is recognizing that percentage growth compounds - each month's 50% increase is applied to the new total (including previous growth), not just the original amount. This creates exponential rather than linear growth.