# Painful bone metastases are common in advanced prostate cancer. Physicians often order treatment with strontium-89 (89Sr)

Painful bone metastases are common in advanced prostate cancer. Physicians often order treatment with strontium-89 (89Sr), a radionuclide with a strong affinity for bone tissue. A patient is given a sample containing 4 mCi of ${89}^{Sr}$.
If 20% of the ${89}^{Sr}$ remains in the body after 90 days, write a function of the form $Q\left(t\right)=Q0{e}^{-kt}$ to model the amount Q(t) of radioactivity in the body t days after the initial dose.
b. what is the biological half-life of ${89}^{Sr}$ under this treatment? Round to the nearest tenth of a day.

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d2saint0
a. $Q\left(t\right)=Qo{e}^{-0.017882t}$
b. t~39 days