The function h gives the altitude of a weather balloon, in meters, where t is the number of minutes after...

1. TRANSLATE the function information

• Given information:
  • \(\mathrm{h(t)}\) = altitude of weather balloon in meters
  • \(\mathrm{t}\) = number of minutes after balloon begins descent
  • \(\mathrm{h(0) = 4,500}\)
• What this tells us: We need to interpret what happens when \(\mathrm{t = 0}\) and the function value is 4,500

2. INFER what the input value means

• Since \(\mathrm{t}\) represents "minutes after descent begins"
• \(\mathrm{t = 0}\) means 0 minutes have passed since descent began
• This is the exact moment the descent starts

3. TRANSLATE the complete statement

• \(\mathrm{h(0) = 4,500}\) means: "At the moment descent began, the altitude was 4,500 meters"
• This matches choice (B) exactly

Answer: (B) The balloon's altitude was 4,500 meters when it began its descent.

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Confusing the input value with the output value

Students see "\(\mathrm{h(0) = 4,500}\)" and focus on the zero, thinking it means the altitude is zero. They mix up what the input (\(\mathrm{t = 0}\)) represents versus what the output (4,500) represents.

This may lead them to select Choice (A) (altitude was 0 meters).

Second Most Common Error:

Poor TRANSLATE reasoning: Misinterpreting the meaning of 4,500 in context

Students correctly identify that \(\mathrm{t = 0}\) is the starting point, but then interpret 4,500 as something other than altitude - like thinking it represents a rate of change or duration.

This may lead them to select Choice (C) (rate of 4,500 meters per minute) or Choice (D) (total of 4,500 minutes).

The Bottom Line:

Function interpretation problems require careful attention to what each part of the notation represents. The input tells you WHEN, and the output tells you WHAT VALUE the function has at that time.