${?}_6^{14}C$ has a half life of $5730$ years. Calculate the fraction $($or percent$)$ of ${?}_6^{14}C$ remaining after an interval of $2000$

years.

Calculate the fraction $($or percent$)$ of ${?}_6^{14}C$ remaining after a decay interval of three half$-$lives.

Calculate the decay interval $("$age$")$ when:

a$)91\%$ of the ${?}_6^{14}C$ remains

b$)9\%$ of the ${?}_6^{14}C$ remains

Calculate the age of a chemical system containing a radioactive nuclide P whose half$-$life is $5\mathrm{.}00{10}^6$ years,

given that the ratio $\frac{D^{**}}{P}$ presently equals $1\mathrm{.}75.$