Problem-Solving and Data AnalysisVery hardChoosing an exponential model from a table
Problem-Solving and Data Analysis practice question
The table shows the amount y of a medicine, in milligrams, in a patient's blood x hours after a dose. x | y 0 | 100 1 | 90 2 | 81 3 | 72.9 Which equation best models the relationship?
- A. y = 100(0.9)ˣCorrect
- B. y = 100 − 10x
- C. y = 100(0.1)ˣ
- D. y = 90x + 100
Answer: A. y = 100(0.9)ˣ
Each value is 0.9 times the previous one: exponential decay with factor 0.9.
Why the other answers are wrong
- B. y = 100 − 10x
- A linear model would give 80 at x = 2, not 81.
- C. y = 100(0.1)ˣ
- This would give 10 at x = 1.
- D. y = 90x + 100
- This increases.
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