The isotope technetium-99m is used by doctors to image the skeleton and heart muscles. Fol- lowing...
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The isotope technetium-99m is used by doctors to image the skeleton and heart muscles. Fol- lowing injection, the concentration of this isotope decays exponentially in the body. a. Let N(t) represent the number of Technetium-99m isotopes present in a person's body t hours after injection. Propose a differential equation that can be used to model the decay of Technetium-99m in the body. Your model should include an unknown constant that controls the exponential growth rate. b. Solve your differential equation from (a) with the initial condition N(0) = No, where No rep- resents the initial amount of Technetium-99m in the body. c. Suppose a third of the initial technetium-99m remains in the body after 10 hours have past. What is the half-life of technetium-99m? Don't forget units in your answer! d. What percent of technetium-99m remains in the body 1 day after injection? The isotope technetium-99m is used by doctors to image the skeleton and heart muscles. Fol- lowing injection, the concentration of this isotope decays exponentially in the body. a. Let N(t) represent the number of Technetium-99m isotopes present in a person's body t hours after injection. Propose a differential equation that can be used to model the decay of Technetium-99m in the body. Your model should include an unknown constant that controls the exponential growth rate. b. Solve your differential equation from (a) with the initial condition N(0) = No, where No rep- resents the initial amount of Technetium-99m in the body. c. Suppose a third of the initial technetium-99m remains in the body after 10 hours have past. What is the half-life of technetium-99m? Don't forget units in your answer! d. What percent of technetium-99m remains in the body 1 day after injection?
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