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MMLU-Pro / 8632 / One model for the spread of an epidemic is that the rate of spread is jointly…

Problem

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

question

One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of 5000 inhabitants, 160 people have a disease at the beginning of the week and 1200 have it at the end of the week. How long does it take for 80%80 \% of the population to become infected?
Plain-text mathematical notation (without MathML)
One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of 5000 inhabitants, 160 people have a disease at the beginning of the week and 1200 have it at the end of the week. How long does it take for 80% of the population to become infected?
Original LaTeX notation
One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of 5000 inhabitants, 160 people have a disease at the beginning of the week and 1200 have it at the end of the week. How long does it take for $80 \%$ of the population to become infected?

category

math

options

  1. 22 days
  2. 20 $\mathrm{days}$
  3. 12 days
  4. 18 days
  5. 8 days
  6. 30 days
  7. 25 $\mathrm{days}$
  8. 10 $\mathrm{days}$
  9. 15 $\mathrm{days}$
  10. 35 days

src

scibench-calculus

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Source and history

upstream_id / Original problem ID
8632
task_id
df2416be-a614-5ecb-a1c2-818e361cfd72
task_key
default--test--8632
task_revision_id
1
config / split
default / test

Official source

initial import