Engineering Board Exam Reviewer · Applications: Growth and Decay · medium

The population of a town grows at a rate proportional to its current size. It increases from 10,000 to 12,000 in 5 years. What is the population after 15 years?

  1. 16000
  2. 14400
  3. 17280
  4. 20736

Answer

C. 17280

Solution

P=P0ekt and e5k=12000/10000=1.2. After 15 years: P=10000(1.2)3=17,280.

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  3. A bacterial culture grows exponentially from 500 to 2000 cells in 6 hours. How many cells are there after 9 hours?
  4. A radioactive substance has a half-life of 10 days. What percent of the original amount remains after 25 days?
  5. A population grows according to dP/dt=kP. If the population doubles in 10 years, find k.
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  7. A bacteria culture grows exponentially and triples in 5 hours. Find the growth constant k in dP/dt=kP.
  8. A radioactive isotope has a decay constant k=0.05 per year. Find its half-life.
  9. Money is invested at a continuously compounded interest rate of 6% per year (dA/dt=rA). How long will it take for the investment to double?
  10. A population of bacteria starts at 500 and grows exponentially with k=0.3 per hour. Find the population after 4 hours.

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