Final answer:
To calculate the remaining mass after 12 minutes for an element that decays at a rate of 11.2% per minute, the exponential decay formula is used, resulting in approximately 71.8 grams remaining.
Step-by-step explanation:
To find the remaining mass of an element that decays at a rate of 11.2% per minute after 12 minutes, we can use the formula for exponential decay:
M = M_0 \times (1 - r)^t
where:
- M is the remaining mass after time t,
- M_0 is the initial mass,
- r is the decay rate per minute,
- t is the time in minutes.
We have:
- Initial mass M_0 = 460 grams,
- Decay rate r = 11.2% or 0.112,
- Time t = 12 minutes.
Substituting these values into the formula gives:
M = 460 \times (1 - 0.112)^{12}
Calculating the remaining mass:
M = 460 \times (0.888)^{12}
M ≈ 71.8 grams
Therefore, the remaining mass after 12 minutes, to the nearest tenth of a gram, is 71.8 grams which corresponds to option b) 71.8 grams.