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# Average word problem

The U.S. annula per-capita consumption of broccoli was 3.1 lb in 1990. By 2007, this amount had risen to 5.5lb. Find the average rate of change in the consumption of broccoli from 1990 to 2007. Show all work

### 3 Answers by Expert Tutors

IBRAHIM A. | Educated Tutor For Excellent Grades in Various SubjectsEducated Tutor For Excellent Grades in V...
4.9 4.9 (12 lesson ratings) (12)
1
Hi Theresa,

x1 = 1990

y1 = 3.1

x2 = 2007

y2 = 5.5

Rate  =  (y2 - y1)  /  (x2 - x1)

= (5.5 - 3.1) / (2007 - 1990)

use your calculator to solve this and that is your rate. God bless.
Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
5.0 5.0 (438 lesson ratings) (438)
1
The average rate of change in broccoli consumption will be the slope of the straight line connecting the two points (1990, 3.1 lbs) and (2007, 5.5 lbs).  The slope is computed as the change in y (broccoli consumption) over the change in x (years).

slope (average rate of change of broccoli consumption) = (5.5-3.1)/(2007-1990) = 2.4/17 = 0.14 pounds (lbs) per year increase

To verify:

3.1 lbs+ (0.14 lbs per year)(17 years) = 3.1 lbs + 2.4 lbs = 5.5 lbs
Kayla S. | Math Tutor specializing in Algebra, Geometry, and TrigonometryMath Tutor specializing in Algebra, Geom...
5.0 5.0 (4 lesson ratings) (4)
1
The rate of change is equal to the change in "y" over the change in "x".

To find the average rate of change in this story problem, we need to find the change in consumption of broccoli divided by the change in the years (or number of years).  The consumption of broccoli is our "y" and the year is our "x."

So the rate of change in the consumption of broccoli = [(consumption in 2007)-(consumption in 1990)]/(2007-1990)

=(5.5-3.1)/(2007-1990)

Then solve the equation. The rate of change should be positive since the consumption of broccoli is increasing every year. It is important to remember that the rate of change is simply the slope.