Answer:
time taken is equal to 14,156 years
Explanation:
we know,
[tex]Y=Ae^{-kt}[/tex]
at t = 0
Y(0) = A
given that half life of plutonium 239 = 24,200
[tex]\dfrac{A}{2}=Ae^{-kt}\\0.5=e^{-kt}\\k\times 24200 = ln(2)\\k = \dfrac{ ln(2)}{24200}[/tex]
[tex]Y=Ae^{-kt}[/tex]
[tex]\frac{3}{2} = e^{-kt}\\ln(1.5)=-\dfrac{ ln(2)}{24200}\times t\\t=-\dfrac{ln(1.5)\times 24200}{ ln(2)}\\t=14,156 \ years[/tex]
hence time taken is equal to 14,156 years
