Brooke purchased a new home and is eager to create a lush, green lawn. To achieve this, she bought a large bag of grass seed to reseed her yard. First, she will spread the seed evenly over the lawn, and then she will set up a sprinkler to water it.

Question

There is a linear relationship between the lawn area Brooke has covered with grass seed, in square feet, and the amount of seed left in the bag, in pounds.
Lawn area (square feet) Amount of seed left (pounds)
100 9
200 8
300 7
400 6
Describe the rate of change for this relationship.
The amount of seed left in the bag
by
per square foot of lawn.

Answer 1

To describe the rate of change for the relationship between the lawn area covered with grass seed and the amount of seed left in the bag, we can analyze the data provided.

We see that as the lawn area increases by 100 square feet, the amount of seed left decreases by 1 pound. Thus, we can calculate the rate of change.

The rate of change can be defined as:

\[ \text{Rate of Change} = \frac{\text{Change in Amount of Seed Left (pounds)}}{\text{Change in Lawn Area (square feet)}} \]

From the data:

• From 100 sq ft to 200 sq ft: 9 lbs to 8 lbs (decrease of 1 lb)
• From 200 sq ft to 300 sq ft: 8 lbs to 7 lbs (decrease of 1 lb)
• From 300 sq ft to 400 sq ft: 7 lbs to 6 lbs (decrease of 1 lb)

We can take any of these intervals; let's focus on the interval from 100 to 200 sq ft:

\[ \text{Rate of Change} = \frac{-1 \text{ lb}}{100 \text{ sq ft}} = -0.01 \text{ lbs/sq ft} \]

Therefore, the rate of change for this relationship is:

The amount of seed left in the bag decreases by 0.01 pounds for every square foot of lawn covered.