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Lesson: Exponential Decay Model

Worksheet: Exponential Decay Model • 11 Questions

Q1:

A scientist begins with 100 mg of a radioactive substance that decays exponentially. After 35 hours, 50 mg of the substance remains. How many milligrams will remain after 54 hours? If necessary, round your answer to 2 decimal places.

Q2:

A doctor injected a patient with 13 milligrams of radioactive dye that decays exponentially. After 12 minutes, there were 4.75 milligrams of dye remaining in the patient’s system. Which of the following is an appropriate model for this situation?

  • A
  • B
  • C
  • D

Q3:

At the start of an experiment, a scientist has a sample which contains 250 milligrams of a radioactive isotope. The radioactive isotope decays exponentially, so that after 250 minutes there are only 32.0 milligrams of the isotope left.

Write the mass of isotope in milligrams, , as a function of the time in minutes, , since the experiment started. Give your answer in the form , rounding and to three significant figures.

  • A
  • B
  • C
  • D
  • E

Find the half-life of the isotope, giving your answer to the nearest minute.

  • A94 minutes
  • B76 minutes
  • C84 minutes
  • D122 minutes
  • E4 minutes

Q4:

The rate at which a radioactive substance decays is proportional to the remaining number of atoms. The differential equation which can be used to describe this process follows: represents the number of atoms remaining after seconds. The proportionality constant is considered the decay constant for this process. If represents the number of remaining atoms at seconds, find the general solution.

  • A
  • B
  • C
  • D

Q5:

A quantity decays in time years according to the formula . If half the amount is left after 46 years, what is the value of ?

  • A2
  • B
  • C
  • D
  • E
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