6

Set 2: Exponential Functions

Explanation

Answer: A

Uranium-235 has a half-life of 704 million years. What fraction remains after 2,112 million years?

A.

18\frac{1}{8}

✓ Correct
B.

14\frac{1}{4}

C.

12\frac{1}{2}

D.

116\frac{1}{16}

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Calculate using half-lives. 1. Half-lives: 2112704=3\frac{2112}{704} = 3 half-lives. 2. Remaining: (12)3=18(\frac{1}{2})^3 = \frac{1}{8}. 3. Result: 18\frac{1}{8} of original amount remains. Strategic Tip: 3 half-lives = (12)3=18(\frac{1}{2})^3 = \frac{1}{8}. Choice B is incorrect because this is after 2 half-lives. Choice C is incorrect because this is after 1 half-life. Choice D is incorrect because this would be after 4 half-lives.

Key Steps:

The correct answer is 18\frac{1}{8}

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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