Find the amount of Vanadium that has decayed after 74 days as a percent.

Question

Vanadium-48 has a half life of 16 days

Answer 1

A = a₀ - a₀(0.5)^74/16

A = a₀ - a₀(0.5)^4.625

A = a₀ - a₀(0.040)

A = 0.96a₀

Answer 2

V(t) = V₀·(0.5)^t/16

• V(t) = the amount of Vanadium left after t days
• V₀ = the initial amount of Vanadium
• t = days = 74

 

V(t) = V₀·(0.5)^t/16

V(74) = V₀·(0.5)^74/16

V(74) = V₀·0.0405

 

As a percent:

 

(V(74)/V₀)·100% = (V₀·0.0405/V₀)·100% = 4.05%

Answer 3

A(t) = A(0) (1/2)^t/16, t in days

 

A(74) = A(0) (1/2)^74/16 ≅ 0.040526 A(0)

 

You are left with 0.040526 times the initial amount, which is 4.0526% of the initial amount.  Then the amount that decayed is (100 - 4.0526)% = 95.9474%.