7

Set 6: Exponential Functions (Intermediate)

Explanation

Answer: A

Calculate the value of y=100(0.5)3y = 100(0.5)^3.

A.

12.5

✓ Correct
B.

25

C.

50

D.

150

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Perform the exponentiation first. 1. Exponent: (0.5)3=0.5×0.5×0.5=0.125(0.5)^3 = 0.5 \times 0.5 \times 0.5 = 0.125. 2. Multiply: 100×0.125=12.5100\times 0.125 = 12.5. Strategic Tip: 0.55 is 1/21 /2. (1/2)3=1/8(1/2)^3 = 1/8. 100/8=12.5100 /8 = 12.5. Choice B is incorrect because it represents 2 half-lives (1005025100\to 50 \to 25). Choice C is incorrect because it represents 1 half-life.

Key Steps:

The correct answer is 12.5

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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