Average word problem

Question

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

Answer 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.

Answer 2

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.

Answer 3

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