To find the rate of change of the height of the candle as it burns, we can analyze the data you provided. Here's the information you gave in a clearer format:
- At 1 hour, the height is 7 inches.
- At 2 hours, the height is 6 inches.
- At 3 hours, the height is 5 inches.
- At 4 hours, the height is 4 inches.
Now, let's calculate the change in height per hour:
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From 1 to 2 hours:
- Change in height = 6 inches - 7 inches = -1 inch.
- Rate of change = -1 inch / 1 hour = -1 inch per hour.
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From 2 to 3 hours:
- Change in height = 5 inches - 6 inches = -1 inch.
- Rate of change = -1 inch / 1 hour = -1 inch per hour.
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From 3 to 4 hours:
- Change in height = 4 inches - 5 inches = -1 inch.
- Rate of change = -1 inch / 1 hour = -1 inch per hour.
The rate of change is constant throughout the burning time, indicating that the height of the candle decreases linearly.
Overall, the height decreases by 1 inch per hour.