Set 6: Exponential Functions

Explanation

Answer: A

Which function represents a value that decreases by 50% each year?

$y = 100(0.5)^t$

✓ Correct

$y = 100(1.5)^t$

$y = 100(50)^t$

$y = 100(0.05)^t$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Decrease of 50% means factor is 0.5. 1. Identify Rate: $r = 0.50$ . 2. Calculate Factor: $b = 1 - 0.50 = 0.50$ . 3. Equation: $y = 100(0.5)^t$ . Strategic Tip: Losing 50% is the same as keeping 50%. This is also called half-life. Choice B is incorrect because 1.5 means 50% growth. Choice D is incorrect because 0.05 means losing 95%.

Key Steps:

•

The correct answer is $y = 100(0.5)^t$

Why others are wrong:

B: Choice B 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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