1. Section 9.2 Cross Sectional Modeling & Rates of Change

2. Idea

3. Graphical Idea Consider the tract of Missouri Farmland from the previous section. If y is held constant at a value of 1, the cross-section model would be the formula of the trace shown in the graph below. What type of model seems appropriate? This model would be labeled.

4. Graphical Idea Consider the tract of Missouri Farmland from the previous section. If x is held constant at a value of 0.8, the cross-section model would be the formula of the trace shown in the graph below. What type of model seems appropriate? This model would be labeled.

5. Tabular Idea To construct a cross-section model from a two-way table, find the row or column which represents the value of x or y that is being held constant. If x is being held constant, then the y values become the inputs (L1) and the z values become the outputs (L2). After looking at the scatterplot, the most appropriate regression model is found. If y is being held constant, then the x values become the inputs (L1) and the z values become the outputs (L2). After looking at the scatterplot, the most appropriate regression model is found.

6. Example 1a The table below shows the average weight gain/loss of a pig measured in kg/day as a function of its mass m in kg and the air temperature T in  C. Find an appropriate cross- section model and use it to estimate and interpret the value of.

7. Example 1b The table below shows the average weight gain/loss of a pig measured in kg/day as a function of its mass m in kg and the air temperature T in  C. Find an appropriate cross- section model and use it to estimate and interpret the value of.

8. Example 1c The table below shows the average weight gain/loss of a pig measured in kg/day as a function of its mass m in kg and the air temperature T in  C. Use an appropriate cross- section model to estimate and interpret.

9. Example 2a The table below shows the function = the population (in millions) and projected population of Americans age A years old in various years. For modeling purposes, y = years since 1990. Find a formula for. What does this function model? Use this model to estimate and interpret the value of and of.

10. Example 2b The table below shows the function = the population (in millions) and projected population of Americans age A years old in various years. For modeling purposes, y = years since 1990. Find a formula for. What does this function model? Use this model to estimate and interpret the value of and of.

11. Formula Idea If we have the formula of, we can plug in a specific value of x or a specific value of y to get a cross- section model.

12. Example 3a Consider the function having formula. Find a formula for.

13. Example 3b Consider the function having formula. Find a formula for.

14. Example 3c Consider the function having formula. Find a formula for.

15. Example 3d Consider the function having formula. Find a formula for.

16. Example 4a The future value of an investment of 1 million dollars with an annual yield of r% after T years is given by million dollars. Find a simplified formula for. What does this function model?

17. Example 4b The future value of an investment of 1 million dollars with an annual yield of r% after T years is given by million dollars. Evaluate and interpret.

18. Example 4c The future value of an investment of 1 million dollars with an annual yield of r% after T years is given by million dollars. Find a simplified formula for. What does this function model?

19. Example 4d The future value of an investment of 1 million dollars with an annual yield of r% after T years is given by million dollars. Evaluate and interpret.