Set 14: Exponential Functions

Explanation

Answer: B

Which function represents exponential decay?

$y = 0.5(3)^x$

$y = 4(0.99)^x$

✓ Correct

$y = 2(1.01)^x$

$y = -5x + 2$

Detailed Explanation

Choice B is correct. Choice B is the correct answer. Decay occurs when the base $0< b < 1$ . 1. Check A: Base is 3 ( $>1$ , Growth). 2. Check B: Base is 0.99 ( $<1$ , Decay). 3. Check C: Base is 1.01 ( $>1$ , 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.

Key Steps:

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The correct answer is $y = 4(0.99)^x$

Why others are wrong:

A: Choice A is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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