Question

The table illustrates the decay occurring in a 352-gram sample of vanadium-49 as time progresses.



Approximately how many grams of vanadium-49 will remain after a span of 1,320 days?

(1 point)
Responses

22
22

32
32

11
11

43

Answer 1

To determine how many grams of vanadium-49 will remain after 1,320 days, we need the half-life of vanadium-49. Vanadium-49 has a half-life of approximately 330 days. This means that every 330 days, half of the remaining vanadium-49 will decay.

1. Calculate the number of half-lives in 1,320 days:
\[
\text{Number of half-lives} = \frac{1320 \text{ days}}{330 \text{ days/half-life}} = 4
\]

2. Start with the initial amount of vanadium-49:
\[
\text{Initial amount} = 352 \text{ grams}
\]

3. After each half-life, the remaining amount is halved. Therefore, after 4 half-lives:
- After 1st half-life: \( 352 \div 2 = 176 \) grams
- After 2nd half-life: \( 176 \div 2 = 88 \) grams
- After 3rd half-life: \( 88 \div 2 = 44 \) grams
- After 4th half-life: \( 44 \div 2 = 22 \) grams

Thus, after 1,320 days, approximately 22 grams of vanadium-49 will remain.

**The correct response is: 22**