1. **State the problem:** Sheri has $515.85 saved and saves $62 each week. We need to write a function for her total savings over time, discuss the domain, and find how many weeks to reach $1795.00. 2. **Write the function rule:** Let $w$ be the number of weeks. Sheri's total savings $S(w)$ is the initial amount plus $62$ times the number of weeks: $$S(w) = 515.85 + 62w$$ 3. **Discuss the domain:** The domain represents possible values of $w$. Since $w$ is the number of weeks, it must be a whole number greater than or equal to zero (no negative or fractional weeks). So, the domain is $w \in \{0,1,2,3,\dots\}$, not all real numbers. 4. **Find weeks to save $1795.00$:** Set $S(w) = 1795$ and solve for $w$: $$1795 = 515.85 + 62w$$ Subtract 515.85 from both sides: $$1795 - 515.85 = 62w$$ $$1279.15 = 62w$$ Divide both sides by 62: $$w = \frac{1279.15}{62} \approx 20.63$$ Since $w$ must be a whole number of weeks, Sheri needs to save for 21 weeks to have at least $1795.00$. **Final answers:** - Function: $S(w) = 515.85 + 62w$ - Domain: $w$ is a whole number $\geq 0$ - Weeks to save $1795$: 21 weeks