3
advanced-math

Which function represents exponential decay?

A

y=0.5(3)xy = 0.5(3)^x

B

y=4(0.99)xy = 4(0.99)^x

C

y=2(1.01)xy = 2(1.01)^x

D

y=−5x+2y = -5x + 2

Correct Answer: B

Choice B is the correct answer. Decay occurs when the base 0<b<10 < b < 1.

  1. Check A: Base is 3 (>1>1, Growth).
  2. Check B: Base is 0.99 (<1<1, Decay).
  3. Check C: Base is 1.01 (>1>1, Growth).
  4. Check D: Linear function.

💡 Strategic Tip: Even if it's close to 1 (like 0.99), if it's less than 1, it's decay.

Choice A is incorrect because the base is 3, not 0.5 (which is the initial value). Choice C is incorrect because 1.01 is greater than 1.

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Set 23: Exponential Functions 23