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

True statements: A, B, and C.

Why:
- A: The yearly decay factor ≈ 5132/5500 ≈ 0.9331, so half-life = ln(0.5)/ln(0.9331) ≈ 10 years (≈10.0), so after ~10 years about half remains.
- B: The largest listed amount is at t = 0, A = 5,500 g, so the maximum is 5,500 g.
- C: A decreases as t increases (5500, 5132, 4788, 4467, 4168).

Why D and E are false:
- D: The changes over equal 1-year intervals are not constant (−368, −344, −321, −299), so not the same number of grams.
- E: Loss from 0→1 is 368 g, from 1→2 is 344 g; 344 is not approximately half of 368.