2
advanced-math

Which function has a graph that increases faster as xx gets larger?

Function A: y=100(1.5)xy = 100(1.5)^xFunction B: y=50(2)xy = 50(2)^x

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.

  1. Function A: Base b=1.5b = 1.5.
  2. Function B: Base b=2b = 2.
  3. Comparison: 2>1.52 > 1.5, so Function B grows faster despite smaller initial value.
  4. Long-term: As xx \to \infty, 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.