A radioactive isotope has a half-life of 20 days, and decays continuously.

Question

a. Express the amount of an initial 100-gram sample that will remain radioactive, 𝐴(𝑡), as a function of the number of days, 𝑡.

b.Based on our knowledge of the half-life, we would expect that after 40 days, 25 grams of the initial sample would remain active. Verify this with the function that you created by evaluating 𝐴(40). Show your computation.

Answer 1

(a)

A(t) = A₀ (0.5)^t/20

t = days

A₀ = 100 g

A(t) = (100 g) (0.5)^t/20

(b)

A(40) = (100 g) (0.5)^40/20 = 25 g