Question

Order the following nine steps to building a mathematical model?

A. Formulate the model, Test the model, Define the problem, Gather data, Validate the model, Analyze the results, Implement the model, Choose the model, Interpret the results
B. Define the problem, Gather data, Choose the model, Formulate the model, Validate the model, Implement the model, Analyze the results, Interpret the results, Test the model
C. Define the problem, Formulate the model, Gather data, Validate the model, Analyze the results, Implement the model, Interpret the results, Choose the model, Test the model
D. Gather data, Define the problem, Validate the model, Choose the model, Formulate the model, Implement the model, Analyze the results, Interpret the results, Test the model

Answer 1

The correct answer to ordering the steps for building a mathematical model is option B, which outlines the steps in a logical sequence that aligns with the principles of the scientific method and effective problem-solving.

Step-by-step explanation:

The correct answer is option B. Building a mathematical model involves a structured approach much like the scientific method. This approach not only helps in understanding the world and solving problems, but it also ensures that the model is applicable and reliable. Here is the ordered process that aligns with the scientific method and problem-solving approaches:

1. Define the problem: Much like asking a question in the scientific method, this step establishes the foundation for the model.
2. Gather data: This corresponds with researching existing sources and collecting information relevant to the problem.
3. Choose the model: Selecting the appropriate modeling approach is critical for the accurate representation of the problem.
4. Formulate the model: Similar to formulating a hypothesis, this step turns the problem definition into a mathematical framework.
5. Validate the model: Ensuring that the model accurately reflects the real-world situation is akin to testing the hypothesis in science.
6. Implement the model: This step involves putting the model into practice to see how it works in real scenarios.
7. Analyze the results: Look at the results obtained from the model to see if they are logical and accurate.
8. Interpret the results: Understanding the implications of the results is key to evaluating the success of the model.
9. Test the model: Finally, comprehensive testing determines if the model holds up under various conditions, and if it can be trusted for decision-making.

An example of a mathematical model could be using a set of equations to predict traffic flow based on current and historical traffic data.