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advanced-mathWhich function has a graph that increases faster as gets larger?
Function A: Function B:
A
Function B
B
Function A
C
They increase at the same rate
D
Cannot determine
Correct Answer: A
Choice A is the correct answer. Compare growth factors.
- Function A: Base .
- Function B: Base .
- Comparison: , so Function B grows faster despite smaller initial value.
- Long-term: As , the base matters more than the coefficient.
💡 Strategic Tip: Larger base = faster exponential growth in the long run.
Choice B is incorrect because Function A has a smaller base. Choice C is incorrect because different bases mean different growth rates. Choice D is incorrect because we can compare the bases.