Advanced MathHardBase of an exponential through two points
Advanced Math practice question
The graph of the exponential function h(x) = a · bˣ, where a and b are positive constants, passes through the points (0, 3) and (2, 12). What is the value of b?
Answer: 2
At x = 0: a · b⁰ = a = 3. At x = 2: 3b² = 12, so b² = 4 and b = 2 (positive).
Common wrong answers
- If you answered 3
- 3 is a, the value at x = 0, not the base.
- If you answered 4
- 4 is b², one step short. Take the square root.
- If you answered 4.5
- 4.5 is 12/3 halved or (12 − 3)/2 — treating the function as linear. It multiplies by b each step.
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