Maria is using her phone, and the function \(\mathrm{g(t) = -2t + 100}\) approximates the battery percentage remaining after t...

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{g(t) = -2t + 100}\)
  • t represents hours of phone use (\(\mathrm{t \geq 0}\))
  • g(t) represents battery percentage remaining
• We need to find the meaning of the y-intercept

2. INFER what the y-intercept represents

• The y-intercept occurs when the input variable equals zero
• In this context: when \(\mathrm{t = 0}\) (zero hours of use)
• This represents the starting condition before any phone use

3. Calculate the y-intercept value

• Substitute \(\mathrm{t = 0}\) into the function:
  \(\mathrm{g(0) = -2(0) + 100}\)
  \(\mathrm{g(0) = 100}\)
• The y-intercept is \(\mathrm{(0, 100)}\)

4. TRANSLATE the mathematical result to context

• \(\mathrm{t = 0}\) means "when she started using it" (no time has passed)
• \(\mathrm{g(0) = 100}\) means "100% battery remaining"
• Therefore: The phone had 100% battery when she started using it

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse the slope and y-intercept values and their meanings.

They see the coefficient -2 in the function and think this relates to the y-intercept question, leading them to focus on "2% battery loss per hour." They don't recognize that the question specifically asks about the y-intercept (the constant term 100), not the rate of change (slope -2).

This may lead them to select Choice A (Maria's phone loses approximately 2% battery per hour).

Second Most Common Error:

Inadequate INFER reasoning: Students don't connect \(\mathrm{t = 0}\) to the real-world meaning of "starting condition."

They might calculate \(\mathrm{g(0) = 100}\) correctly but fail to understand that \(\mathrm{t = 0}\) represents the initial moment before any phone use began. Without this connection, they can't properly interpret what the 100% represents in context.

This leads to confusion and guessing among the remaining choices.

The Bottom Line:

This problem requires students to distinguish between different parts of a linear function (slope vs y-intercept) and connect the mathematical concept of "when input equals zero" to its real-world meaning as an initial or starting condition.