The population density of Iceland, in people per square kilometer of land area, increased from 2.5 in 1990 to 3.3...

1. TRANSLATE the problem information

• Given information:
  • Population density in 1990: \(2.5\text{ people per km}^2\)
  • Population density in 2014: \(3.3\text{ people per km}^2\)
  • Land area: \(100,250\text{ km}^2\)
• What we need to find: Population increase (not total population)

2. INFER the most efficient approach

• Key insight: Population = Density × Area
• We can find the increase in two ways:
  • Method 1: Calculate the density increase, then multiply by area
  • Method 2: Calculate population for each year, then find the difference

3. SIMPLIFY using Method 1 (recommended)

• Density increase = \(3.3 - 2.5 = 0.8\text{ people per km}^2\)
• Population increase = \(0.8 \times 100,250 = 80,200\text{ people}\) (use calculator)

Answer: D. 80,200

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students correctly calculate the 2014 population (\(3.3 \times 100,250 = 330,825\)) but fail to recognize that the question asks for the increase in population, not the final population value.

This leads them to select Choice A (330,825) instead of finding the difference between 2014 and 1990 populations.

Second Most Common Error:

Inadequate SIMPLIFY execution: Students understand the concept but make arithmetic errors when multiplying decimals by large numbers, or they perform incorrect operations like dividing instead of multiplying.

This may lead them to select Choice B (132,330) or Choice C (125,312), depending on the specific calculation error.

The Bottom Line:

This problem tests whether students can distinguish between calculating a final value versus calculating a change. The key is recognizing that "increase" means finding the difference, not just the ending amount.