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An element with mass 460 grams decays at 11.2% per minute? What is the remaining mass after 12 minutes, to the nearest tenth of a gram?

a) 127.9 grams
b) 71.8 grams
c) 89.5 grams
d) 69.6 grams

User Pup
by
7.5k points

1 Answer

1 vote

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.

User Seb Jachec
by
8.2k points
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