Painful bone metastases are common in advanced prostate cancer. Physicians often order treatment with strontium$-89(($:${?}^{89}Sr\},$ a radionuclide with a strong affinity for bone tissue. A patient is given a sample containing $4$mCi of ${?}^{89}Sr.$

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$($a$)$ If $20\%$ of the ${?}^{89}Sr$ remains in the body after $85$ days, write a function of the form $Q(t)=Q_0{e}^{-kt}$ to model the amount $Q(t)$ of radioactivity in the body $t$ days after the initial dose. Round the value of $k$ to five decimal places. Do not round intermediate calculations.

$Q(t)=$