Respuesta :
Answer:
The answer to the question is
It will be ≅ 28.8 years until only 35 % of the substance remains
Explanation:
To solve this we note the required relations and the given variables thus
The half life of the substance is
N(t) = N(0) × [tex](\frac{1}{2} )^{\frac{t}{t_{\frac{1}{2} } } }[/tex]
Thus when only 35% is remaining we have
35% of N(0) = N(0)× [tex](\frac{1}{2} )^{\frac{t}{t_{\frac{1}{2} } } }[/tex]
or 0.35 = [tex](\frac{1}{2} )^{\frac{t}{t_{\frac{1}{2} } } }[/tex] , to solve the previous equation, we take the log of both sides thus
Log (0.35) = Log ( [tex](\frac{1}{2} )^{\frac{t}{t_{\frac{1}{2} } } }[/tex] ) or [tex]\frac{t}{t_{\frac{1}{2} } }[/tex]× log (1/2) =log(0.35)
⇒ [tex]\frac{t}{t_{\frac{1}{2} } }[/tex] = 1.515 and since [tex]t_{\frac{1}{2} }[/tex] = 19 years we have
t = 19 × 1.515 = 28.776 Years
Therefore it will be 28.776 years before 35 % of the substance will be remaining
