Question 1
A radioactive substance decomposes at a rate proportional to the amount present.
Initially there are 40 g, and after 15 years, 80% of the original amount remains.
1.1 Let 𝑀0 be the initial mass. Formulate and solve a differential equation to model the
mass 𝑀(𝑡)after time 𝑡. State any assumptions.
1.2 Determine the amount remaining after 25 years.
Question 2
A sample of Uranium decomposes at a rate proportional to the amount present. Initially
there are 120 g, and after 10 years, 15% of the original amount has decomposed.
2.1 Let 𝑀0 be the initial mass. Formulate and solve the differential equation describing
the decay.
2.2 Find the amount remaining after 18 years.
Question 3
A radioactive isotope has an initial mass of 90 g. After 6 days, 65% of the original
amount remains.
3.1 Formulate and solve the differential equation for the mass.
3.2 Calculate the amount remaining after 15 days.
Question 4
An unstable element decays at a rate proportional to its current mass. Initially there are
150 g, and after 12 hours, 25% of the original mass has decomposed.
4.1 Formulate and solve the differential equation.
4.2 Determine the amount remaining after 30 hours.
Question 5
A radioactive chemical initially has a mass of 75 g. After 9 years, 85% of the original
amount remains.
5.1 Derive the differential equation governing the decay.
5.2 Calculate the remaining mass after 20 years.
Question 6
A radioactive isotope decays proportionally to its present mass. Initially there are 200 g,
and after 16 years, 35% of the original amount has decomposed.
6.1 Develop and solve the differential equation.
6.2 Find the amount remaining after 25 years.
Question 7
A radioactive sample initially has 100 g. After 5 days, 70% of the original mass
remains.
7.1 Formulate and solve the differential equation describing the decay.
7.2 Determine the mass after 14 days.
Question 8
A sample initially contains 250 g of a radioactive material. After 18 months, 22% of the
original amount has decomposed.
A radioactive substance decomposes at a rate proportional to the amount present.
Initially there are 40 g, and after 15 years, 80% of the original amount remains.
1.1 Let 𝑀0 be the initial mass. Formulate and solve a differential equation to model the
mass 𝑀(𝑡)after time 𝑡. State any assumptions.
1.2 Determine the amount remaining after 25 years.
Question 2
A sample of Uranium decomposes at a rate proportional to the amount present. Initially
there are 120 g, and after 10 years, 15% of the original amount has decomposed.
2.1 Let 𝑀0 be the initial mass. Formulate and solve the differential equation describing
the decay.
2.2 Find the amount remaining after 18 years.
Question 3
A radioactive isotope has an initial mass of 90 g. After 6 days, 65% of the original
amount remains.
3.1 Formulate and solve the differential equation for the mass.
3.2 Calculate the amount remaining after 15 days.
Question 4
An unstable element decays at a rate proportional to its current mass. Initially there are
150 g, and after 12 hours, 25% of the original mass has decomposed.
4.1 Formulate and solve the differential equation.
4.2 Determine the amount remaining after 30 hours.
Question 5
A radioactive chemical initially has a mass of 75 g. After 9 years, 85% of the original
amount remains.
5.1 Derive the differential equation governing the decay.
5.2 Calculate the remaining mass after 20 years.
Question 6
A radioactive isotope decays proportionally to its present mass. Initially there are 200 g,
and after 16 years, 35% of the original amount has decomposed.
6.1 Develop and solve the differential equation.
6.2 Find the amount remaining after 25 years.
Question 7
A radioactive sample initially has 100 g. After 5 days, 70% of the original mass
remains.
7.1 Formulate and solve the differential equation describing the decay.
7.2 Determine the mass after 14 days.
Question 8
A sample initially contains 250 g of a radioactive material. After 18 months, 22% of the
original amount has decomposed.
