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MMLU-Pro / 8768 / Newton's law of cooling states that the temperature of an object changes at a…

Problem

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

question

Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 200∘F200^{\circ} \mathrm{F} when freshly poured, and $1 \mathrm{~min}$ later has cooled to 190∘F190^{\circ} \mathrm{F} in a room at 70∘F70^{\circ} \mathrm{F}, determine when the coffee reaches a temperature of 150∘F150^{\circ} \mathrm{F}.
Plain-text mathematical notation (without MathML)
Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 200^(∘)F when freshly poured, and $1 \mathrm{~min}$ later has cooled to 190^(∘)F in a room at 70^(∘)F, determine when the coffee reaches a temperature of 150^(∘)F.
Original LaTeX notation
Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of $200^{\circ} \mathrm{F}$ when freshly poured, and $1 \mathrm{~min}$ later has cooled to $190^{\circ} \mathrm{F}$ in a room at $70^{\circ} \mathrm{F}$, determine when the coffee reaches a temperature of $150^{\circ} \mathrm{F}$.

category

math

options

  1. 10.2 min
  2. 7.8 min
  3. 12.0 min
  4. 9.5 min
  5. 2.8 min
  6. 4.5 min
  7. 5.2 min
  8. 8.4 min
  9. 3.3 min
  10. 6.07 min

src

scibench-diff

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Source and history

upstream_id / Original problem ID
8768
task_id
fa8126f4-f872-5735-9e0b-cbac2d477e99
task_key
default--test--8768
task_revision_id
1
config / split
default / test

Official source

initial import