Which function exhibits exponential decay for all ?

Answer and explanation

Correct answer: D.

  1. Step 1: An exponential function exhibits decay when and the base satisfies .
  2. Step 2: For , and , which satisfies , so it decays.
  3. Step 3: In contrast, grows because ; grows; has a negative base and is not an exponential function on the reals.
Answer
.
Why not the others: '' represents exponential growth; '' has a negative exponent making the effective base (growth); '' has an alternating signed base.

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