The graph shows the prices of different numbers of bushels of corn at a store in the current year. The table shows the prices of different numbers of bushels of corn at the same store in the previous year.

Previous Year

Number of Bushels, Price of Corn (dollars)

3, 21

6, 42

9, 63

12, 84

Part A: Describe in words how you can find the rate of change of a bushel of corn in the current year, and find the value.

Part B: How many dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year? Show your work.

A) Rate of change: 8$/bushel

B) 1$/bushel more

Step-by-step explanation:

A)

The rate of change of a function is defined as:

where

is the change in the y-variable

is the change in the x-variable

The rate of change of a function in a graph also corresponds to the slope of the graph.

Here we want to find the rate of change of the function for the current year, which is represented by the graph.

To have the most accurate estimate, we can take two extreme points (initial and final point of the graph), then calculate the  ratio between increment in y and increment in x.

In this case:

Initial point: (0,0)

Final point: (18,144)

Therefore, the rate of change is:

So, the rate of change for the current year is 8$/bushel.

B)

To answer this part, we have to find the rate of change of the previous year, and then compare the two rates of change.

For the previous year, we can find the rate of change by taking the two extreme points from the table, which are:

(3,21)

(12,84)

Therefore, the rate of change of the previous year was:

which means 7$/bushel.

From part A, we know that for the current year it is

m = 8$/bushel

Therefore, the price of a bushel of corn for the current year is 1$ more (per bushel) than the previous year.