An airplane descends from an altitude of 9,500text{ feet} to 5,000text{ feet} at a constant rate of 400text{ feet per...

Step-by-Step Solution

1. TRANSLATE the problem information

• Given information:
  • Starting altitude: 9,500 feet
  • Ending altitude: 5,000 feet
  • Rate: 400 feet per minute (constant)
  • Need to find: type of function modeling altitude vs time

2. INFER the function type from the rate description

• 'Constant rate' is the key phrase here
• When something changes at a constant rate, it means the same amount of change happens in every equal time period
• This constant rate of change is the defining characteristic of a linear function
• Exponential functions have rates that change over time - they don't have constant rates

3. INFER the direction of the function

• The airplane 'descends' from 9,500 feet to 5,000 feet
• This means altitude is getting smaller as time increases
• A function where the output values decrease as input values increase is called 'decreasing'

Answer: B. Decreasing linear

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may confuse 'constant rate' with exponential growth or decay because they associate airplanes with rapid changes or think 'rate' always means exponential.

They might think: 'Airplanes change altitude quickly, so this must be exponential' or 'Any rate of change means exponential function.'

This may lead them to select Choice A (Decreasing exponential).

Second Most Common Error:

Poor TRANSLATE reasoning: Students correctly identify the function as linear but miss the direction, focusing only on the numbers (9,500 to 5,000) without connecting 'descends' to 'decreasing function.'

They might think: 'It's linear because of constant rate, but I'm not sure about increasing vs decreasing.'

This causes them to get stuck and potentially guess between Choice B (Decreasing linear) and Choice D (Increasing linear).

The Bottom Line:

This problem tests whether students can distinguish between function types based on rate descriptions and connect real-world direction words to mathematical function behavior.