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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 22 centimeters. After 33 hours of burning, its height is 12.5 centimeters. What is the height of the candle after 32 hours?

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 1414 hours of burning, a candle has a height of 2222 centimeters. After 3333 hours of burning, its height is 1212.55 centimeters. What is the height of the candle after 3232 hours?

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Full solution

Q. 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 1414 hours of burning, a candle has a height of 2222 centimeters. After 3333 hours of burning, its height is 1212.55 centimeters. What is the height of the candle after 3232 hours?
  1. Identify Points and Variables: Identify the points given and the variable names:\newlineLet t t be the time in hours and h h be the height in centimeters. We have two points: (1414, 2222) and (3333, 1212.55).
  2. Calculate Slope: Calculate the slope (m m ) of the line using the formula m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1} :\newlinem=12.5−2233−14=−9.519=−0.5 m = \frac{12.5 - 22}{33 - 14} = \frac{-9.5}{19} = -0.5
  3. Use Point-Slope Form: Use the point-slope form of the equation of a line to find the equation. Using point (1414, 2222) and slope −0-0.55:\newlineh−22=−0.5(t−14) h - 22 = -0.5(t - 14) \newlineh=−0.5t+7+22 h = -0.5t + 7 + 22 \newlineh=−0.5t+29 h = -0.5t + 29
  4. Substitute to Find Height: Substitute t=32 t = 32 into the equation to find h h :\newlineh=−0.5(32)+29 h = -0.5(32) + 29 \newlineh=−16+29 h = -16 + 29 \newlineh=13 h = 13 centimeters

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