Set 2: Exponential Functions (Intermediate)

Explanation

Answer: C

Which function represents a quantity that starts at 500 and decreases by 20% each year?

$Value Depreciation$

$y = 500(0.20)^t$

$y = 500(1.20)^t$

$y = 500(0.80)^t$

✓ Correct

$y = 20(500)^t$

Detailed Explanation

Choice C is correct. Choice C is the correct answer. Convert percentage decrease to a decay factor. 1. Identify Rate: Decrease of 20% means $r = 0.20$ . 2. Calculate Factor: $b = 1 - r = 1 - 0.20 = 0.80$ . 3. Form Equation: $y = 500(0.80)^t$ . Strategic Tip: If you lose 20%, you keep 80%. The factor is what you keep. Choice A is incorrect because 0.20 would mean losing 80% per year. Choice B is incorrect because 1.20 represents a 20% increase. Choice D is incorrect because it has the wrong structure entirely.

Key Steps:

•

The correct answer is $y = 500(0.80)^t$

Why others are wrong:

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

B: Choice B 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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Set 2: Exponential Functions (Intermediate)

Detailed Explanation

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