Question

A substance is subject to radioactive decay. The function below shows the relationship between
, the amount of the substance remaining in grams, and
, the number of years the substance has been decaying.



The table below shows several values of
that correspond to time
.

t (years) A (grams)
0 5,500
1 5,132
2 4,788
3 4,467
4 4,168
Which statements are true? Select three that apply.

A.
After 10 years, one-half of the substance will remain compared to its initial value.

B.
The maximum amount of the substance is 5,500 grams.

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C.
The value of
decreases as the value of
increases.

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D.
Over equal time intervals, the value of
changes by the same number of grams.

E.
The amount of substance lost between 1 and 2 years is equal to approximately half the amount of substance lost between 0 and 1 year

Answer 1

Correct answers: A, B, and C.

Brief justification:
- A: The yearly ratio is 5132/5500 ≈ 0.93309, and (0.93309)^10 ≈ 0.5, so the half-life ≈ 10 years.
- B: A is largest at t = 0 (5500 g), so the maximum amount is 5,500 g.
- C: The table values decrease as t increases (5500 → 5132 → 4788 → 4467 → 4168).

D is false because the absolute changes are not equal (368, 344, 321, 299). E is false because the loss from 1 to 2 years (≈344 g) is not about half the loss from 0 to 1 year (≈368 g).