Question

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 14 hours of burning, a candle has a height of 26.2 centimeters. after 33 hours of burning, its height is 22.4 centimeters. what is the height of the candle after 23 hours?

Explanation:

Identify the given data points

Let \(t\) represent the burning time in hours, and \(h(t)\) represent the height of the candle in centimeters.

$$ (t_1, h_1) = (14, 26.2) $$

$$ (t_2, h_2) = (33, 22.4) $$

Calculate the rate of change

$$ m = \frac{h_2 - h_1}{t_2 - t_1} = \frac{22.4 - 26.2}{33 - 14} = \frac{-3.8}{19} = -0.2 $$

Find the height at the target time

Using the point-slope form with \(t = 23\):

$$ h(23) - h_1 = m(23 - t_1) $$

$$ h(23) - 26.2 = -0.2(23 - 14) $$

$$ h(23) = 26.2 - 0.2(9) = 26.2 - 1.8 = 24.4 $$

Answer:

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 14 hours of burning, a candle has a height of 26.2 centimeters. After 33 hours of burning, its height is 22.4 centimeters. What is the height of the candle after 23 hours?

<blank>24.4</blank> centimeters