110k views
1 vote
In the previous problem, you wrote equations that were models of a real-life situation. Models are usually not perfect representations, but they are useful for describing real-life behavior and for making predictions. You predicted when the two trees would be the same height.

a. What are an appropriate domain and range for the two models of tree growth?
b. Where can you find they-intercepts of the model on the graph, in the table, and in the equation? In the situation of the story, what does they-intercept represent?

User Slolife
by
7.3k points

1 Answer

3 votes

Final answer:

The domain for tree growth models should be the time interval of observation, and the range would include the trees' heights within that interval. Y-intercepts can be found on the graph where the line crosses the y-axis, in a table as a value when the independent variable is zero, and in the equation as the constant term. In tree growth scenarios, the y-intercept represents the initial height of a tree at planting.

Step-by-step explanation:

When it comes to determining an appropriate domain and range for models of tree growth, the domain would typically consist of the time intervals during which the tree growth is observed. For example, from the time of planting to a certain number of years after. The range would be the possible heights that the trees can achieve within that time frame.

For the y-intercept, this can be found on the graph where the line crosses the y-axis, in the table as the value of the dependent variable when the independent variable is zero, and in the equation as the constant term (assuming the equation is in the form of y = mx + b where b is the y-intercept). In the context of tree growth, the y-intercept represents the initial height of the tree at the time of planting.

If a line in the model has a larger y-intercept, graphically, it would mean the line shifts up while maintaining parallelism with the original line. Conversely, a smaller y-intercept would mean the line shifts down but remains parallel to the original line. This variation in intercepts can be critical in comparing the initial states between two different models or scenarios.

User Elsunhoty
by
7.7k points