1. **State the problem:** We are given two scenarios involving rates of change: cold and hot beverage sales over months, and football team earnings and budget balance related to ticket sales and table rentals. 2. **Part 1a: Rate of change of cold beverages and hot beverages** - Cold beverages start at 7,200 in July and decrease by 750 per month. - Rate of change for cold beverages is therefore $-750$ cups/month (negative because it decreases). - Hot beverages are given by $y = 900x + 3300$, where $x$ is months after July. - The rate of change for hot beverages is the coefficient of $x$, which is $900$ cups/month. 3. **Part 1b: Which rate of change is greater and meaning** - Compare $|-750| = 750$ and $900$. - $900 > 750$, so hot beverages increase faster than cold beverages decrease. - This means hot beverage sales are growing more rapidly than cold beverage sales are declining. 4. **Part 2a: Rate of change for money earned by football team** - Equation: $y = 15x$, where $y$ is money earned, $x$ is tickets sold. - Rate of change is $15$ dollars per ticket. - This means each ticket sold adds 15 dollars to earnings. 5. **Part 2b: Rate of change of budget balance** - Budget balance decreases as tables rented increase: from 900 to 876 to 852 to 828. - Change per table: $876 - 900 = -24$, $852 - 876 = -24$, $828 - 852 = -24$. - Rate of change is $-24$ dollars per table rented. - This means each table rental reduces the budget balance by 24 dollars. 6. **Part 2c: Compare earnings and spending per table** - One table seats 8 guests, so tickets per table = 8. - Earnings per table: $15 \times 8 = 120$ dollars. - Spending per table: 24 dollars. - Since $120 > 24$, the team earns more from ticket sales per table than it spends on table rentals. **Final answers:** - 1a: Cold beverages rate = $-750$ cups/month, Hot beverages rate = $900$ cups/month. - 1b: Hot beverage rate is greater; hot sales increase faster than cold sales decrease. - 2a: Rate of change for money earned = $15$ dollars/ticket. - 2b: Rate of change of budget balance = $-24$ dollars/table. - 2c: Team earns more from ticket sales per table than it spends on rentals.