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Advanced MathMediumExtrapolating an exponential table back to zero

Advanced Math practice question

The table gives values of an exponential function g. x | g(x) 1 | 6 2 | 18 3 | 54 What is the value of g(0)?

Answer: 2

Each step multiplies by 3, so g(x) = 2 · 3ˣ. Going back one step from g(1) = 6 divides by 3: g(0) = 2.

Common wrong answers

If you answered 0
0 assumes the function passes through the origin; exponential functions never reach 0.
If you answered 3
3 is the growth factor, not g(0).
If you answered -6
−6 subtracts 12 (the difference 18 − 6) as if the function were linear.

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