(Solved): This exercise uses the radioactive decay model. The haif-life of radium-226 is 1600 years. Suppose ...

This exercise uses the radioactive decay model. The haif-life of radium-226 is 1600 years. Suppose we have a 24-mg sample. (a) Find a function $$m(t)=m_0{2}^{?t/h}$$ that models the mass remaining after $$t$$ years. $$m(t)=$$ (b) Find a function $$m(t)=m_0{e}^{?rt}$$ that models the mass remaining after $$t$$ years. (Round your $$r$$ value to six decimal places.) $$m(t)=$$ (c) How much of the sample will remain after 4500 years? (Round your answer to one decimal place.) $$\mathrm{mg}$$ (d) After how many years will only $$15\mathrm{mg}$$ of the sample remain? (Round your answer to one decimal place.) exercise uses the radioactive decay model. half-life of cesium-137 is 30 years. Suppose we have a $$12?9$$ sample. (a) Find a function $$m(t)=m_0{2}^{?t/h}$$ that models the mass remaining after $$t$$ years. $$m(t)=$$ (b) Find a function $$m(t)=m_0{e}^{?rt}$$ that models the mass remaining after $$t$$ years. (Round your $$r$$ value to four decimal places.) $$m(t)=$$ (c) How much of the sample will remain after 77 years? (Round your answer to one decimal place.) $$9$$ (d) After how many years will only $$4g$$ of the sample remain? (Round your answer to the nearest whole number.) yr This exercise uses Newton's Law of Cooling. A hot bowl of soup is served at a dinner party. It starts to cool according to Newton's Law of cooling so that its temperature at time $$c$$ is given by $$T(t)=67+144e^{?0.05t}$$ where $$t$$ is measured in minutes and $$T$$ is measured in " $$F_2$$ (a) What is the initial temperature of the soup? of (b) What is the temperature after 10 min? (Round your answer to one decimal place.) $${\mathrm{oF}}^{\mathrm{F}}$$ (c) After how long will the temperature be $$100^{?}\mathrm{F}$$ ? (Round your answer to the nearest whole number.) min