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AlgebraMediumInterpreting linear models

Algebra practice question

A phone's battery percentage is modeled by P = 100 − 8t, where t is the number of hours since it was unplugged. What does 8 represent?

  1. A. The battery percentage when unplugged
  2. B. The number of hours the battery lasts
  3. C. The percentage the battery drops each hourCorrect
  4. D. The starting battery percentage

Answer: C. The percentage the battery drops each hour

In P = 100 − 8t, the coefficient of t is the rate of change: the battery falls 8 percentage points per hour. The constant 100 is the starting percentage (choices A/D).

Why the other answers are wrong

A. The battery percentage when unplugged
That's the constant 100, the value of P when t = 0 — the 8 is attached to t, so it describes change over time, not a starting value.
B. The number of hours the battery lasts
The battery would hit 0 at t = 12.5 hours, not 8; the 8 is the rate of drop per hour, not a duration.
D. The starting battery percentage
The starting percentage is the constant 100 (when t = 0). The 8 multiplies t, so it tells you how fast P changes.

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