Problem-Solving and Data AnalysisVery hardChoosing between linear and exponential from ratios
Problem-Solving and Data Analysis practice question
x (bounces): 0, 1, 2, 3
y (height, cm): 100, 70, 49, 34.3
The table shows the height y, in centimetres, to which a ball rises after x bounces. Which equation best models the relationship?
- A. y = 100(0.7)ˣCorrect
- B. y = 100 − 30x
- C. y = 100(0.3)ˣ
- D. y = 70 − 21x
Answer: A. y = 100(0.7)ˣ
Each bounce keeps 70% of the previous height (70/100 = 49/70 = 34.3/49 = 0.7), so the model is exponential with factor 0.7 and initial value 100.
Why the other answers are wrong
- B. y = 100 − 30x
- 100 − 30x fits the first two points but predicts 40 at x = 2, not 49.
- C. y = 100(0.3)ˣ
- 0.3 is the share LOST each bounce; the height keeps 0.7.
- D. y = 70 − 21x
- 70 − 21x gives 70 at x = 0, but the height before any bounce is 100.
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