College Algebra & Trigonometry, 2018a

3.5. APPLICATIONS OF THE NEGATIVE EXPONENTIAL FUNCTION 185
Exercises 3.5
1) If the half-life of radioactive cesium-137 is 30 years, find the value of k in the
equation A(t) =A 0 e −kt .
a) Given a 10 gram sample of cesium-137, how much will remain after 80
years?
b) How long will it take for only 2 grams of cesium-137 to remain?
2) The half-life for radioactive thorium-234 is about 25 days. Use this to find
the value of k in the equation A(t) =A 0 e −kt .
a) How much of a 40 gram sample will remain after 60 days?
b) After how long will only 10 grams of thorium-234 remain?
3) Given a sample of strontium-90, it is known that after 18 years there are
32mg remaining and after 65 years there are 10mg remaining. Use this information
to find out how much strontium-90 was in the sample to begin with, and also
determine the half-life of strontium-90.
4) A 12 mg sample of radioactive polonium decays to 7.26 mg in 100 days.
a) What is the half-life of polonium?
b) How much of the 12 mg sample remains after 180 days?