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

glamrockqueen7 2021-09-22 Answered

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 \(\displaystyle{89}^{{{S}{r}}}\).
If 20% of the \(\displaystyle{89}^{{{S}{r}}}\) remains in the body after 90 days, write a function of the form \(\displaystyle{Q}{\left({t}\right)}={Q}{0}{e}^{{−{k}{t}}}\) 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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Expert Answer

d2saint0
Answered 2021-09-23 Author has 18556 answers
a. \(\displaystyle{Q}{\left({t}\right)}={Q}{o}{e}^{{-{0.017882}{t}}}\)
b. t~39 days
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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 \(\displaystyle{89}^{{{S}{r}}}\).
If 20% of the \(\displaystyle{89}^{{{S}{r}}}\) remains in the body after 90 days, write a function of the form \(\displaystyle{Q}{\left({t}\right)}={Q}{0}{e}^{{−{k}{t}}}\) to model the amount Q(t) of radioactivity in the body t days after the initial dose.
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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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