b. t~39 days

asked 2021-05-02

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.

asked 2021-05-12

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.

asked 2021-06-24

The following question consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells. Assume that for a population K=1000 and α=0.05.. Draw the directional field associated with this differential equation and draw a few solutions. What is the behavior of the population?

asked 2021-09-22

asked 2021-08-16

The following question consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells. When does population increase the fastest in the threshold logistic equation \(\displaystyle{P}'{\left({t}\right)}={r}{P}{\left({1}-{\frac{{{P}}}{{{K}}}}\right)}{\left({1}-{\frac{{{T}}}{{{P}}}}\right)}?\)

asked 2021-07-31

The following question consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells. When does population increase the fastest for the Gompertz equation

\(\displaystyle{P}{\left({t}\right)}'=\alpha{\ln{{\left({\frac{{{K}}}{{{P}{\left({t}\right)}}}}\right)}}}{P}{\left({t}\right)}?\)

\(\displaystyle{P}{\left({t}\right)}'=\alpha{\ln{{\left({\frac{{{K}}}{{{P}{\left({t}\right)}}}}\right)}}}{P}{\left({t}\right)}?\)

asked 2021-05-07

The following question consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells. [T] The Gompertz equation has been used to model tumor growth in the human body. Starting from one tumor cell on day 1 and assuming α=0.1α=0.1 and a carrying capacity of 10 million cells, how long does it take to reach “detection” stage at 5 million cells?