What is the height of the candle after 16 hours?

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 8 hours of burning, a candle has a height of 20.4 centimeters. After 19 hours of burning, its height is
18.2 centimeters. What is the height of the candle after 16
hours?

Answer 1

Let Y = height

Let X = time

 

Height is a linear function of time, so Y = mX + b, where m is the slope and b is the y-intercept.  

 

We can calculate the slope from the given values (8,20.4) and (19,18.2) 

 

Slope = (y2 - y1) / (x2 - x1) = (18.2 - 20.4) / (19 - 8) = -2.2 / 11 = -0.2 

 

This means that the height of the candle is going down by 0.2 cm per hour

 

Since 16 hours is 8 hours after the first data point of (8,20.4), the height will go down by 8 * (-0.2) = -1.6 cm in the 8 hours between hour 8 and hour 16.  

 

So the height of the candle after 16 hours = 20.4 - 1.6 = 18.8 centimeters