To determine the rate of change of the amount of fence Max painted, we can look at the given data. The rate of change can be calculated by finding the difference in the amount painted over the difference in time.
From the provided information, we can see the following amounts painted over each minute:
- After 1 minute: 3.5 square feet
- After 2 minutes: 7 square feet
- After 3 minutes: 10.5 square feet
- After 4 minutes: 14 square feet
- After 5 minutes: 17.5 square feet
To find the rate of change, we can calculate the change in square feet painted divided by the change in minutes:
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From minute 1 to minute 2: \[ \text{Change in square feet} = 7 - 3.5 = 3.5 \] \[ \text{Change in minutes} = 2 - 1 = 1 \] \[ \text{Rate of change} = \frac{3.5}{1} = 3.5 \text{ square feet per minute} \]
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From minute 2 to minute 3: \[ \text{Change in square feet} = 10.5 - 7 = 3.5 \] \[ \text{Change in minutes} = 3 - 2 = 1 \] \[ \text{Rate of change} = \frac{3.5}{1} = 3.5 \text{ square feet per minute} \]
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From minute 3 to minute 4: \[ \text{Change in square feet} = 14 - 10.5 = 3.5 \] \[ \text{Change in minutes} = 4 - 3 = 1 \] \[ \text{Rate of change} = \frac{3.5}{1} = 3.5 \text{ square feet per minute} \]
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From minute 4 to minute 5: \[ \text{Change in square feet} = 17.5 - 14 = 3.5 \] \[ \text{Change in minutes} = 5 - 4 = 1 \] \[ \text{Rate of change} = \frac{3.5}{1} = 3.5 \text{ square feet per minute} \]
Thus, the rate of change of the amount of fence Max painted is consistent at 3.5 square feet per minute throughout the time intervals provided.
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