1. **State the problem:** We need to find the monthly revenue function $R(x)$ for a city where each resident pays a base fee plus a variable fee depending on water usage. 2. **Given information:** - Base fee per resident: 5.04 - Variable fee: 1.52 per 1000 gallons - Maximum usage considered: 4000 gallons (or 4 in thousands) - Number of customers: 469,000 3. **Define variables:** Let $x$ be the total number of gallons used in thousands by one customer, where $0 \leq x \leq 4$. 4. **Write the revenue function for one customer:** $$R_{single}(x) = 5.04 + 1.52x$$ 5. **Calculate total revenue for all customers:** Since there are 469,000 customers, total revenue is: $$R(x) = 469000 \times (5.04 + 1.52x)$$ 6. **Simplify the expression:** $$R(x) = 469000 \times 5.04 + 469000 \times 1.52x$$ $$R(x) = 2,363,760 + 712,880x$$ 7. **Final revenue function:** $$\boxed{R(x) = 2363760 + 712880x}$$ This function gives the total monthly revenue in terms of $x$, the thousands of gallons used per customer (up to 4).