Answer :
The ddt in the soil with half-life of 12 years needs 44.4 years to decompose.
We need to know about the half-life of the radioactive elements to solve this problem. The radioactive element will decay over time and follow the equation
N = No(1/2)^(t/t'')
where N is the final quantity, No is the initial quantity, λ is the decaying constant, t is time and t'' is the half-life of a radioactive element.
From the question above, we know that
t'' = 12 yr
N = 15 ppbm
No = 195
By substituting the given parameter, we can calculate the required for decomposing
N = No(1/2)^(t/t'')
15 = 195(1/2)^(t/12)
1/13 = (0.5) ^ (t/12)
t/12 = ⁰'⁵log(1/13)
t/12 = 3.7
t = 44.4 years
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