The calculated rate of change, 6, affirms the specified relationship between the number of nurseries (n) and the trees to be planted near athletic fields (t). The consistency validates the given scenario.
In the given scenario, the rate of change is specified as 6, and it is associated with the number of nurseries (n) that donate trees. The equation provided for measuring the rate of change is:
Rate of change = (Change in dependent variable) / (Change in independent variable)
In this context, the dependent variable is the number of trees to be planted near the athletic fields (t), and the independent variable is the number of nurseries that donate trees (n). The rate of change is given as 6, and it is mentioned that the coefficient of n is 6.
So, the equation representing the relationship between the number of nurseries (n) and the number of trees to be planted near the athletic fields (t) is:
Rate of change = (6t) / n
Given that n is 6 (the number of nurseries) and t is 27 (the number of trees to be planted near the athletic fields), we can substitute these values into the equation to find the rate of change:
6 = (6 * 27) / 6
Solving for the rate of change:
6 = 162 / 6
6 = 27
This implies that the rate of change is 6, as given in the problem statement. Therefore, the relationship between the number of nurseries donating trees and the number of trees to be planted near the athletic fields is consistent with the specified rate of change.
Complete question:
Read the following description of a relationship:
A principal asked some local nurseries to each donate 6 trees to her school. The plan is to plant 9 trees in the student garden and the rest near the athletic fields.
Let n represent the number of nurseries that donate trees and t represent the number of trees to be planted near the athletic fields.
This relationship can also be shown in a table. Complete the equation that represents the relationship between n and t.