standard_description: Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
problem_activity: Task
Below is a table showing the approximate boiling point of water at different elevations:
| Elevation (meters above sea level) | Boiling Point (degrees Celsius) |
|------------------------------------|---------------------------------|
|                 0                  |               100               |
|                500                 |              98.2               |
|                1000                |              96.5               |
|                1500                |              94.7               |
|                2000                |              93.1               |
|                2500                |              91.3               |
Based on the table,
if we were to model the relationship between the elevation and the boiling point of water, would a linear function be appropriate? Explain why or why not.
Below are some additional values for the boiling point of water at higher elevations:
| Elevation (meters above sea level) | Boiling Point (degrees Celsius) |
|------------------------------------|---------------------------------|
|               5,000                |              83.2               |
|               6,000                |              80.3               |
|               7,000                |              77.2               |
|               8,000                |              74.3               |
|               9,000                |              71.5               |
Based on the table,
if we were to model the relationship between the elevation and the boiling point of water, would a linear function be appropriate? Explain why or why not.
When the information from both tables is combined, would a linear function be appropriate to model this data?  What kind of function would you use to model the data?  Why?


aligns: no