Answer:
1400 millon years, it is probable that if the mineral came from igneous rock, ithe rock age would be the same. There were active volcanoes 1400 year ago in proterozoic era.
Explanation:
Lifetime of radiactive compound is calculated with
[tex]ln(\frac{N_t}{N_0})=-kt[/tex] with [tex]N_t:[/tex] mass at time t, [tex]N_0:[/tex] original mass, [tex]k:[/tex] decay constant.
So we know that when 700 millon years pass, the half of original material decays ([tex]\frac{N_t}{N_0})=0.5[/tex]. With that information we can know k.
[tex]ln(0.5)=-k*700[/tex] so, [tex]k=-ln(0.5)/700=0.00099[/tex]
With k, the actual and original quantity of material we can know how old is the rock:
[tex]t=-ln(\frac{N_t}{N_0})/k[/tex] so, [tex]t=-ln(\frac{1000}{4000})/0.00099=1400 millon years[/tex]
([text]N_0=1000+3000[/text] is the actual quantity plus the quantity that decays to Pb-207)
