Predicting order of nucleophilic substitution reactivity
Acetone a is aprotic polar solvent which is often used as solvent for $\ce{S_{N}2}$ reactions (notably in conjunction with $\ce{NaI}$ as in the Finkelstein reaction). For $\ce{S_{N}2}$ reactions steric hindrance and leaving group capability is of great importance, so primary halides will be usually easier replaced by iodine then tertiary.
$\ce{AgNO3}$ will probably react as a base forming nitric acid. Even though nitric acid is a rather strong acid this is more likely than $\ce{NO_3-}$ acting as nucleophile. Besides that, $\ce{Ag+}$ is known to have a unique selectivity for halogens and will attack them readily, forming $\ce{AgX}$ and a carbocation, hence promoting $\ce{E 1}$/$\ce{S_{N}1}$.