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Problem-Solving and Data AnalysisMediumRecognising a linear decrease

Problem-Solving and Data Analysis practice question

A car's value decreases by $1,500 every year. Which type of function best models the car's value over time, and why?

  1. A. A decreasing linear function, because the value falls by the same amount each year.Correct
  2. B. An exponential decay function, because the value is multiplied by the same factor each year.
  3. C. An increasing linear function, because the change is constant.
  4. D. A quadratic function, because the value eventually reaches zero.

Answer: A. A decreasing linear function, because the value falls by the same amount each year.

A constant AMOUNT of change each year is the mark of a linear function; since the value falls, the slope is negative.

Why the other answers are wrong

B. An exponential decay function, because the value is multiplied by the same factor each year.
Exponential decay would mean losing the same PERCENT each year; here the loss is a fixed dollar amount.
C. An increasing linear function, because the change is constant.
The value is falling, so the linear function decreases.
D. A quadratic function, because the value eventually reaches zero.
Reaching zero doesn't make a function quadratic; a falling line reaches zero too.

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