Question

Do the following for the function given below.

(time, cell phone owners in a small town), where time is measured in years after 2000
a. Describe an appropriate domain and range for the function.
b. Make a rough sketch of a graph of the function.
c. Briefly discuss the validity of the graph as a model of the true function.


Part 1
a. Choose the appropriate domain for the function below.

A. The domain is cell phone users during the given years; 500 people to 45,000 people.
B. The domain is cell phone users during the given years; 4 million people to 1.3 billion people.
C. The domain is years from 2000 to 2010; 2000 to 2010, where 2000 is year 0.
D. The domain is years from 2000 to 2010; 0 to 10, where 2000 is year 0.

Answer 1

The appropriate domain for the function would be:

C. The domain is years from 2000 to 2010; 2000 to 2010, where 2000 is year 0.

a. Domain and Range:

Domain: The appropriate domain for the function is time measured in years after 2000. Therefore, the correct choice is:

C. The domain is years from 2000 to 2010; 2000 to 2010, where 2000 is year 0.

Range: The range would represent the number of cell phone owners in a small town during that time frame. However, the given options do not provide information about the range.

b. Graph Sketch:

A rough sketch of the graph would typically show the number of cell phone owners on the y-axis and time (years after 2000) on the x-axis. The graph should start at 2000 (or 0 on the x-axis) and extend to 2010. The specific shape of the graph would depend on the nature of the function, whether it's linear, exponential, etc.

c. Validity of the Graph:

The validity of the graph as a model of the true function depends on the actual trend of cell phone ownership in the small town during the specified time frame. If the graph is based on accurate data and represents the trend reasonably well, it can be considered valid. However, without more information about the function or data, it's challenging to assess its validity definitively. Data accuracy and representation of the actual trend are crucial for the model's validity.