Question

If the half-life of an element is 67 yr and the initial quantity is 3 kg, write a function of the form Q(t) = Q0 e^-kt to model the quantity of the element left after years. Round k to 4 decimal places.

Would appreciate a step by step explanation, thank you.

Answer 1

A0=3kg

t1/2=67y

λ=ln2/t1/2

λ=0.6931/67

λ=0.0103447761-> 0.0103

Final Amount=Aoe^-λ×t

Final Amount=A0e^-0.0103447761×t

You can put the time that you want to find how much of the material has been left after a certain amount of time

as an example

if t=143years

Final Amount=3×e^-0.0103447761×143

Final Amount=3×e^−1.479302982

Final Amount=0.6833892338

A0 is the amount of material that we have before it goes into radioactive decay