Mr. Lee is preparing a community garden project. He will first spend time gathering supplies, and then he will spend additional time planting each type of flower.

Question

There is a linear relationship between the number of flower types planted and the total time spent on the project, in hours.
Describe the rate of change for this relationship.
The time spent on the project
by
per flower type planted.

Answer 1

In Mr. Lee's community garden project, since there is a linear relationship between the number of flower types planted and the total time spent, we can describe the rate of change as follows:

The rate of change represents the amount of time spent on the project per additional flower type planted. If we denote the total time spent on the project as \( T \) (in hours) and the number of flower types planted as \( N \), the rate of change can be expressed as:

\[ \text{Rate of change} = \frac{\Delta T}{\Delta N} \]

This means that for each additional flower type planted, Mr. Lee will spend a fixed amount of time (let's denote this as \( k \) hours) on planting that type. Therefore, the rate of change is the number of hours spent on the project per flower type planted.

If he spends constant \( k \) hours on each flower type, then the total time spent on planting \( N \) flower types would be:

\[ T = \text{(time gathering supplies)} + kN \]

In conclusion, the rate of change is \( k \) hours per flower type planted.