Advanced MathVery hardIdentifying exponential decay from a table
Advanced Math practice question
x: 0, 1, 2, 3
f(x): 96, 48, 24, 12
The table gives values of a function f. Which equation could define f?
- A. f(x) = 96(1/2)ˣCorrect
- B. f(x) = 96 − 48x
- C. f(x) = 96(2)ˣ
- D. f(x) = 48(1/2)ˣ
Answer: A. f(x) = 96(1/2)ˣ
Each step halves the value: 96, 48, 24, 12. That's exponential decay with factor 1/2 and starting value 96: f(x) = 96(1/2)ˣ.
Why the other answers are wrong
- B. f(x) = 96 − 48x
- 96 − 48x is linear: it would give 96, 48, 0, −48.
- C. f(x) = 96(2)ˣ
- 96(2)ˣ doubles each step instead of halving.
- D. f(x) = 48(1/2)ˣ
- 48(1/2)ˣ starts at 48, but f(0) = 96.
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