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MMLU-Pro / 8637 / A radioactive material, such as the isotope thorium-234, disintegrates at a rate…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

A radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the amount currently present. If Q(t)Q(t) is the amount present at time tt, then dQ/dt=−rQd Q / d t=-r Q, where r>0r>0 is the decay rate. If 100mg100 \mathrm{mg} of thorium-234 decays to 82.04mg82.04 \mathrm{mg} in 1 week, determine the decay rate rr.
Plain-text mathematical notation (without MathML)
A radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the amount currently present. If Q(t) is the amount present at time t, then dQ/dt=−rQ, where r>0 is the decay rate. If 100mg of thorium-234 decays to 82.04mg in 1 week, determine the decay rate r.
Original LaTeX notation
A radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the amount currently present. If $Q(t)$ is the amount present at time $t$, then $d Q / d t=-r Q$, where $r>0$ is the decay rate. If $100 \mathrm{mg}$ of thorium-234 decays to $82.04 \mathrm{mg}$ in 1 week, determine the decay rate $r$.

category

math

options

  1. 0.02500 $\text{day}^{-1}$
  2. 0.02222 $\text{day}^{-1}$
  3. 0.04545 $\text{day}^{-1}$
  4. 0.04242 $\text{day}^{-1}$
  5. 0.03030 $\text{day}^{-1}$
  6. 0.02828 $\text{day}^{-1}$
  7. 0.03535 $\text{day}^{-1}$
  8. 0.05050 $\text{day}^{-1}$
  9. 0.02121 $\text{day}^{-1}$
  10. 0.03333 $\text{day}^{-1}$

src

scibench-diff

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Source and history

upstream_id / Original problem ID
8637
task_id
f7e77dcf-0b7e-536b-b64c-b04b192a48d4
task_key
default--test--8637
task_revision_id
1
config / split
default / test

Official source

initial import