What is the decay rate of strontium 90?

Question

Strontium 90 is a radioactive material that  decays  according  to  the  function A (t) = A₀ e^- 0.0244t, where A₀ is the initial amount present and A is the amount present  at  time  t (in  years).  Assume  that  a  scientist  has  a sample of 500 grams of strontium 90.

(a) What is the decay rate of strontium 90?
(b) How much strontium 90 is left after 10 years?
(c) When will 400 grams of strontium 90 be left?
(d) What is the half-life of strontium 90?
                  

Answer 1

Step 1 :

(a)

 The amount of a radioactive material present at time is .

Where is the original amount of the radioactive material and is a negative number that presents a rate of decay.

Find the decay rate of strontium 90 :

 

The function is .

Compare the function with .

The decay rate of strontium 90 is

Step 2 :

(b)

The function is .

Substitute and in the function.

After 10 years, 391.74 grams of strontium 90 be left.

Step 3 :

(c)

The function is .

Substitute and in the function.

After 9.15 years, 400 grams of strontium 90 be left.

Comments

Step 4 :

(d)

The function .

Half-life of the function .

Substitute in the function.

The function is .

Solve for .

Half-life of strontium 90 is 28.4 years.

Solution :

(a) The decay rate of strontium 90 is

(b) After 10 years, 391.74 grams of strontium 90 be left.

(c) After 9.15 years, 400 grams of strontium 90 be left.

(d) Half-life of strontium 90 is 28.4 years.