Todd bought a candle for a Halloween jack-o'-lantern. The candle got shorter as it burned.

Question

There is a linear relationship between the time, in hours, Todd's candle was burning, and its height, in inches.
Time (hours) Height (inches)
1 7
1
4
2 6
1
2
3 5
3
4
4 5
Describe the rate of change for this relationship.
The height
by
per hour.

Answer 1

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:

1. 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.

2. 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.

3. 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.