3
advanced-math

Which of the following functions represents exponential growth?

A

y=50(0.95)xy = 50(0.95)^x

B

y=100(1.05)xy = 100(1.05)^x

C

y=20(0.2)xy = 20(0.2)^x

D

y=200(1)xy = 200(1)^{-x}

Correct Answer: B

Choice B is the correct answer. Exponential growth occurs when the base bb is greater than 1.

  1. Recall: For y=abxy = ab^x, if b>1b > 1, the function grows. If 0<b<10 < b < 1, it decays.
  2. Analyze Choice A: b=0.95<1b = 0.95 < 1 (Decay).
  3. Analyze Choice B: b=1.05>1b = 1.05 > 1 (Growth).
  4. Analyze Choice C: b=0.2<1b = 0.2 < 1 (Decay).
  5. Analyze Choice D: 1x1^{-x} is constant (1), or if interpreted as (1/e)x(1/e)^x it would be decay. But typically 1x=11^x = 1, which is constant.

💡 Strategic Tip: Look strictly at the number inside the parentheses (the base). If it's bigger than 1, it's growth.

Choice A is incorrect because the base 0.95 is less than 1. Choice C is incorrect because the base 0.2 is less than 1. Choice D is incorrect because a base of 1 does not change, or a negative exponent on a base >1>1 would imply decay.