Question

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to cone back to the skipped part. The half-life of cesium-137 is 30 years. Suppose we have a 30 mg sample. Exercise
(a) Find the mass that remains after t years. Step 1 Let y(t) be the mass (in mg) remaining after t years. Then we know the following Stop 2 Since the half-life is 30 years, then y(30) - More Information m Your answer cannot be understood or graded Submit Skie (you cannot come back) Exercise
(b) How much of the sample remains after 20 years? Step 1 After 20 years we have the following (20) 30 mg (Round your answer to two decimal places.)

Answer 1

Answer:

(a)y(t)=30exp(-0.0231t)

(b)y(20)=18.9mg

Step-by-step explanation:

At a particular time t, the mass of a radioactive substance like Cesium-137 is governed by the equation:

N=N₀e⁻ᵏᵗ where k=ln 2/half life

(a)Mass that remains after t years

Half Life= 30 years

k= ln2/30=0.0231

Initial Mass, N₀=30mg

Therefore the mass N that remains at time t

N=N₀e⁻ᵏᵗ

N=30exp(-0.0231t)

y(t)=30exp(-0.0231t)

(b)We want to determine how much of the sample remains after 20 years.

At t=20 years

y(t)=30exp(-0.0231t)

y(20)=30exp(-0.0231X20)

=30 X 0.63

y(20)=18.9mg