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Radioactive decay can be described by the following equation

$lnA=ln{A}_0-kt$

where $A_0$ is the original amount of the substance, $A$ is the amount of the substance remaining after time $t,$ and $k$ is a constant that is characteristic of the substance.

For the radioactive isotope radon$-222,k$ is $1\mathrm{.}81{10}^{-1}$ days ${?}^{-1}.$

If the original amount of radon$-222$ in a sample is $28\mathrm{.}9mg,$ how much time is needed for the amount of radon$-222$ that remains to fall to $19\mathrm{.}0mg?$

days