Strontium 90 is a radioactive material that decays according to the function A(t)= A0e^(−0.02t) where A0 is the initial amount present and A is the amount present at time t(in years).

Question

Assume that a scientist has a sample of 500 grams of strontium 90. Use the information given to complete the 4 part question below:

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) When will half of the initial amount remain?

Answer 1

Hello! We can begin by remembering that the decay formula being used here is of the form:

A(t) = A₀e^-λt where t is time, λ is decay rate (in terms of t) and A₀ is the sample size.

Question 1: What is the decay rate?

Based on the form of your question, your decay value is λ = -0.02 (or -2%) .

Question 2: How much Sr₉₀ is left after 10 years?

Plug in your values: A(t₁₀) = 500*e^-0.02*10 = 409.4 grams

Question 3: When will 400 grams be left?

Same process as question 2, but here A(t) = 400 :

400 = 500*e^-0.02t => Ln(400) = Ln(500*e^-0.02t) => Ln(400) = Ln(500) + Ln(e^-0.02t)

This expression can be simplified to Ln(4/5) = -0.02t => t = 11.16 years

Question 4: When will half of the original sample remain?

Same exact process as we just did, A(t) = 250:

250 = 500*e^-0.02t => Ln(250) = Ln(500*e^-0.02t) => Ln(250) = Ln(500) + Ln(e^-0.02t)

This expression can be simplified to Ln(1/2) = -0.02t => t = 34.66 years