1. The problem states that Shadow's medicine bottle starts with 100 milliliters and each dose is 5 milliliters. 2. The function $M(d)$ represents the amount of medicine left after $d$ doses, so the formula is: $$M(d) = 100 - 5d$$ 3. The domain of $M(d)$ is the set of all possible values of $d$ (the number of doses) that make sense in this context. 4. Since Shadow can only take whole doses, $d$ must be a whole number (integer) starting from 0 (no doses taken) up to the maximum number of doses before the medicine runs out. 5. To find the maximum $d$, solve for when $M(d) = 0$: $$0 = 100 - 5d$$ $$5d = 100$$ $$d = \frac{100}{5} = 20$$ 6. Therefore, $d$ can be any whole number from 0 to 20 inclusive. 7. So, the domain of $M(d)$ is all whole numbers ranging from 0 to 20. Final answer: The domain of $M(d)$ is $\{d \in \mathbb{Z} \mid 0 \leq d \leq 20\}$, which means all whole numbers from 0 to 20.