Advanced MathMediumWorking backwards through a constant ratio
Advanced Math practice question
An exponential function g satisfies g(x + 1) = (1/3) · g(x) for all x, and g(2) = 6. What is the value of g(0)?
Answer: 54
Each step forward divides by 3, so each step back multiplies by 3: g(1) = 18 and g(0) = 54.
Common wrong answers
- If you answered 12
- 12 adds 3 twice, treating the function as linear.
- If you answered 18
- 18 is g(1), one step back.
- If you answered 2/3
- 2/3 goes forward two steps instead of back (6 ÷ 9).
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