Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 5 hours of burning, a candle has a height of 24.5 centimeters. After 23 hours of burning, its height is 22.7 centimeters. What is the height of the candle after 11 hours?

Answer 1

To find the linear function that represents the relationship between the height of the candle and the amount of time it has been burning, we can use the two data points provided: (5, 24.5) and (23, 22.7).

First, find the slope of the linear function using the two data points:
Slope = (22.7 - 24.5) / (23 - 5) = -1.8 / 18 = -0.1

Next, use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
y - 24.5 = -0.1(x - 5)
y - 24.5 = -0.1x + 0.5
y = -0.1x + 25

Now that we have the linear function that represents the height of the candle, we can find the height of the candle after 11 hours:
Height = -0.1(11) + 25
Height = -1.1 + 25
Height = 23.9 centimeters

Therefore, the height of the candle after 11 hours is 23.9 centimeters.