Question

Nina lit a candle and measured its height after different lengths of time. After 0.5 hour, the height of the candle was 16.5 centimeters. After 1.5 hours, the height of the candle was 13.5 centimeters. Assume the relationship is linear. Find and interpret the rate of change.

Options:
A. The rate of change is -3 centimeters per hour, so the height of the candle decreases by 3 centimeters each hour.
B. The rate of change is 3 centimeters per hour, so the height of the candle increases by 3 centimeters each hour.
C. The rate of change is -1 centimeter per hour, so the height of the candle decreases by 1 centimeter each hour.
D. The rate of change is 1 centimeter per hour, so the height of the candle increases by 1 centimeter each hour.

Answer 1

The rate of change for the candle's height over time is -3 centimeters per hour, meaning it decreases by 3 centimeters each hour (option A).

Step-by-step explanation:

To determine the rate of change for the candle's height, we need to calculate the slope of the line that represents the candle's height over time. The formula for slope (rate of change) is the rise over run, which is the change in the dependent variable (height of the candle) divided by the change in the independent variable (time, in hours).

We have two points representing the candle's height at different times: (0.5 hours, 16.5 centimeters) and (1.5 hours, 13.5 centimeters). To find the slope, we subtract the heights and divide by the difference in time. The calculation is as follows:

Rise: Change in height = 13.5 cm - 16.5 cm = -3 cm
Run: Change in time = 1.5 hours - 0.5 hour = 1 hour
Slope (rate of change): -3 cm / 1 hour = -3 cm per hour

Therefore, the rate of change is -3 centimeters per hour. This means the height of the candle decreases by 3 centimeters each hour, as stated in option A.