To find the rate of change for the relationship between the number of flower types planted and the total time spent on the project, we will examine the data points provided:
- 5 flower types planted = 5 hours
- 15 flower types planted = 10 hours
- 25 flower types planted = 15 hours
We can observe that as the number of flower types increases, the time spent on the project also increases. To determine the rate of change (or slope) of this linear relationship, we can apply the formula:
\[ \text{Rate of Change} = \frac{\text{Change in Time}}{\text{Change in Flower Types}} \]
Let's calculate the change between the first two data points:
From 5 flower types to 15 flower types:
- Change in Time = 10 hours - 5 hours = 5 hours
- Change in Flower Types = 15 - 5 = 10 flower types
Now, calculate the rate of change for this segment:
\[ \text{Rate of Change} = \frac{5 \text{ hours}}{10 \text{ flower types}} = 0.5 \text{ hours per flower type} \]
Now, let's verify the rate of change using the second pair of values (15 flower types to 25 flower types):
From 15 flower types to 25 flower types:
- Change in Time = 15 hours - 10 hours = 5 hours
- Change in Flower Types = 25 - 15 = 10 flower types
Calculating the rate for this segment:
\[ \text{Rate of Change} = \frac{5 \text{ hours}}{10 \text{ flower types}} = 0.5 \text{ hours per flower type} \]
Since the rate of change is consistent across the intervals, we conclude that the relationship is indeed linear.
Conclusion: The rate of change for this relationship is 0.5 hours per flower type planted. This means that for each additional type of flower Mr. Lee plants, he will spend an additional 0.5 hours on the project.
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