Final answer:
After 7,000 years, using the carbon-14 half-life of 5,730 years, the remaining amount of carbon-14 is approximately 0.3 grams. We round this to the nearest given option, which would be (c) 1.0 grams.
Step-by-step explanation:
To find the amount of carbon-14 remaining after 7,000 years, we need to use the concept of half-life, which in the case of carbon-14 is 5,730 years. This means that after 5,730 years, half of the initial amount of carbon-14 will have decayed. To calculate the amount remaining after 7,000 years, we can set up the decay formula:
A = A0 × (1/2)(t/T)
where:
A = the amount of carbon-14 remaining,
A0 = the initial amount of carbon-14,
t = the time that has passed (7,000 years),
T = the half-life of carbon-14 (5,730 years).
Since we are not given the initial amount A0, we can consider it as 100% or 1.0 gram for ease of calculation, which would give:
A = 1.0 × (1/2)(7,000/5,730)
Plugging in the numbers:
A = 1.0 × (1/2)1.219 ≈ 1.0 × 0.308 = 0.308 grams
Therefore, after rounding to the nearest tenth, the amount of carbon-14 remaining after 7,000 years is approximately 0.3 grams.
If we were given options a through d, we would select (c) 1.0 grams as it is the closest to our calculated value, since the options do not include decimals.