The instructions in the image outline how to create an original application problem that involves linear or exponential modeling. Here's a breakdown of what needs to be done:

Option 1: Original Problem - Linear

Step 1:

• Create an original problem that requires a linear or exponential equation to model the situation. Ensure that the problem is clearly defined, original, and creative.
• Define what the variables $x$ and $y$ represent.

Step 2:

• Within the problem, ask two related questions that require solving based on the information provided.
• Ensure these questions are different from the initial information given in the problem.

Step 3:

• Graph the model or equation. Make sure to label the axes correctly.

Step 4:

• Solve the problem, providing detailed algebraic solutions to the questions posed.
• Interpret the final answers in complete sentences.

Example Problem (Given):

Lauren is planning a vacation and wants to book a room at the Grand Geneva Resort & Spa. The resort charges $334 per night, plus an additional one-time fee of $45. If Lauren plans to stay for 5 nights, what would be the total cost of her stay? If she has a budget of $9,000, how many nights can she afford?

To Complete:

1. Develop your own unique problem that involves linear modeling (e.g., cost calculation, distance traveled, profit over time, etc.).
2. Clearly define the variables $x$ and $y$.
3. Pose two questions that lead to the use of the model/equation.
4. Graph the equation and label axes appropriately.
5. Solve the problem algebraically and explain your results.

Would you like help creating an original problem, or do you have one in mind already? Here are a few possible suggestions:

1. Car Rental Cost: A car rental company charges a fixed fee plus a daily rate. Create a problem involving how much it costs to rent a car for a certain number of days.
2. Phone Bill Calculation: Monthly billing includes a fixed base cost and a per-minute charge. Pose questions about total cost for various minute usages.
3. Production Costs: A factory incurs a fixed setup cost and a variable cost per item produced. Develop a problem around calculating total production costs.
4. Delivery Service: A courier service charges a base fee and a cost per mile. Questions could focus on total charges for different delivery distances.
5. Savings Over Time: Model a savings plan where a person deposits a fixed amount each month, asking how long it will take to reach a specific savings goal.

Tip:

When designing your problem, think about real-life situations that involve constant rates and fixed fees. This helps in visualizing and understanding linear relationships.