Answer:
k = -0.09165 years^(-1)
Explanation:
The exponential decay model of a radioactive isotope is generally given as;
A(t) = A_o(e^(kt))
Where;
A_o is quantity of isotope before decay, k is decay constant and A(t) is quantity after t years
We are given;
A_o = 5 kg
A(10) = 2kg
t = 10 years
Thus;
A(10) = 2 = 5(e^(10k))
Thus;
2 = 5(e^(10k))
2/5 = (e^(10k))
0.4 = (e^(10k))
In 0.4 = 10k
-0.9164 = 10k
k = -0.9164/10
k = -0.09165 years^(-1)
