Answer:
(a)
The quantity of element that are still contained in the stolen rock
is 37.1627g
(b)
this rock can be used by the superhero's nemesis to render the superhero powerless is 567 years
Step-by-step explanation:
We are given
original quantity =250g
half life time =200 years
so, we can use formula
[tex]P(t)=P_0(0.5)^{\frac{t}{h} }[/tex]
where
Po is initial quantity
h is half life time
t is time in years
so, we can plug h=200 and Po=250
and we get
[tex]P(t)=250(0.5)^{\frac{t}{200} }[/tex]
(a)
we can plug t=550
and then we can find P(t)
[tex]P(550)=250(0.5)^{\frac{550}{200} }[/tex]
we get
[tex]P(550)=37.1627g[/tex]
(b)
we can set P(t)=35
and then we can solve for t
[tex]35=250(0.5)^{\frac{t}{200} }[/tex]
[tex]0.5^{\frac{t}{200}}=\frac{7}{50}[/tex]
we can take ln on both sides
[tex]\ln \left(0.5^{\frac{t}{200}}\right)=\ln \left(\frac{7}{50}\right)[/tex]
[tex]t=\frac{200\ln \left(\frac{7}{50}\right)}{\ln \left(0.5\right)}[/tex]
[tex]t=567.3[/tex]
[tex]t=567[/tex] years
