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Pqpolalk357

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$$\frac{1}{6} \times 10^6 \frac{\mathrm{pCi}}{\mathrm{hr}}$$

(pCi=picocuries). The room contains $$10^6$$ liters of air. (The rate was chosen so that the room reaches the EPA action level of $$4 \frac{pCi}{liter}$$ after $$24$$ hours.) Air in the room is being exchanged with the outside air at a rate of $$R$$ liters/hr. The outside air has a concentration of $$0.5$$ pCi/liter.

Set up an equation for the total radiation $x$ in the room in picocuries, assuming instantaneous uniform mixing, that is, the indoor concentration of radioactivity is $$\frac{x}{10^{6}}$$ pCi/liter.

Explain your equation using the notations $$\Delta x$$ pCi, $$\Delta t$$ hr, and display the units of every variable explicitly to show that they match (e. g., (pCi/liter)(liter/hr) = pCi/hr).

I wanted to try to express the differential equation under the form $$\frac{dx}{dt}=a-bx$$ such that x is the value of the radiation, but I am not sure how to use the remaining information.