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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.) $mg$ (d) After how many years will only $15mg$ 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.) $oF_{F}$ (c) After how long will the temperature be $100_{?}F$ ? (Round your answer to the nearest whole number.) min

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