Advanced MathMediumExponential function from two values
Advanced Math practice question
The function g is defined by g(x) = a · bˣ, where a and b are positive constants. If g(0) = 5 and g(1) = 15, what is the value of g(3)?
Answer: 135
g(0) = a · b⁰ = a = 5. Then g(1) = 5b = 15 gives b = 3. So g(3) = 5 · 3³ = 5 · 27 = 135.
Common wrong answers
- If you answered 35
- 35 is 5 + 10 × 3, treating the function as linear with slope 10. It multiplies by 3 each step: 5, 15, 45, 135.
- If you answered 45
- 45 is g(2) = 5 · 9. The question asks for g(3).
- If you answered 125
- 125 is 5³, cubing a instead of b. It's the base b = 3 that gets raised to the power.
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