10

Set 3: Exponential Functions (Advanced)

Explanation

Answer: A

A substance decays to half its amount every 10 days. If you start with 800 grams, how much remains after 10 days?

A.

400 grams

✓ Correct
B.

200 grams

C.

600 grams

D.

100 grams

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Use the half-life concept. 1. Half-Life: Every 10 days, the amount is multiplied by 0.55. 2. After 10 Days: 800×0.5=400800\times 0.5 = 400 grams. 3. Formula: A(t)=800(0.5)t/10A(t) = 800(0.5)^{t/10} where tt is in days. Strategic Tip: After one half-life period, exactly half remains. Choice B is incorrect because this would be after 20 days (two half-lives). Choice C is incorrect because this is not half of 800. Choice D is incorrect because this would be after 30 days.

Key Steps:

The correct answer is 400 grams

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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