Question

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear? The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees. The rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees. The rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees. The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Answer 1

Answer:

The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees , describes that function is nonlinear

Step-by-step explanation:

Rate of Change between 1 & 2 Trees = (120 - 60)/(2-1)  = 60

Rate of Change between 2 & 3 Trees = (180 - 120)/(3-2)  = 60

Rate of Change between 1 & 3 Trees = (180 - 60)/(3-1)  = 120/2 = 60

Rate of Change between 3 & 4 Trees = (240 - 180)/(4-3)  = 60

Rate of Change between 3 & 5 Trees = (290 - 180)/(5-3)  = 110/2 = 55

The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees , describes that function is nonlinear

Answer 2

Answer:

Concept:

The average rate of change formula is used to find the slope of a graphical function. To find the average rate of change, divide the change in the y value by the change in the x value. Finding the average rate of change is particularly useful for determining the average velocity or change in a measurable quantity, such as the average velocity. The mean rate of change of a function corresponds to the slope of the line connecting the two endpoints of a given interval (called a secant line). The average rate of change of a function is the change in the y value of the numerator and the change in the x value of the denominator. Simplify by subtracting the x, y values ​​of the second point from the x, y values ​​of the first point.

Explanation:

Step 1:

The rate of change between 2 and 3 trees is different from the rate of change between 3 and 5 trees and accounts for the nonlinearity of the change in the function between 2 and 3 trees       = $\frac{(180-120)}{(3-2)}$

                                                                                  = 60.

Step 2:

Rate of change between 1-3 trees =  $\frac{( 180 - 60 )}{( 3 -1)}$

                                                          =  $\frac{( 120 )}{( 260)}$

Step 3:

Rate of change between 3 and 4 trees = $\frac{(240 - 180)}{( 4-3)}$

                                                                  = 60.      

Step 4:                                                                                                                                                              

Change rate of 3-5 trees =  $\frac{(290 - 180)}{(5-3)}$

                                          =  $\frac{( 110 )}{( 2)}$

                                            = 55.

The rate of change of 2-3 trees and the rate of change of 3-5 trees are different. So we can finalise this function as a linear function.

#SPJ2