$3.(5$ marks$)$ To assist in identifying a tumor a patient is injected with $\backslash (400\backslash$mu $\backslash$mathrm$\{$~g$\}\backslash )$ of a radioactive dye. Over time the body metabolizes and breaks the dye down. After one hour there is only $\backslash (100\backslash$mu $\backslash$mathrm$\{$~g$\}\backslash )$ of the dye remaining. Assuming that the amount of the radioactive dye which is metabolized is proportional to the amount still active in the body, set up and solve an initial value problem that models the amount of dye after $\backslash ($ t $\backslash )$ hours.