What is the height of the candle after 14 hours?

Question

After 7 hours of burning, a candle has a height of 24.9 centimeters. After 18 hours of burning, its height is 21.6 centimeters.

Answer 1

Using two point form:

 

(y - 21.6) / (x - 18) = (21.6 - 24.9) / (18 - 7)

(y - 21.6) / (x - 18) = -3.3 / 11

(y - 21.6) / (x - 18) = -0.3

y - 21.6 = -0.3(x - 18)

 

Can you put into slope-intercept form then calculate for x = 14?

 

Answer 2

One thing that is missing from the problem is a statement that the candle height diminishes at a constant rate.  So, that is an assumption.

 

1. Figure out the slope of the candle height.  The height is a function of time.  And we have two points to work with:  (7, 24.9) and (18, 21.6).  Slope m = Y₂ - Y₁ / X₂ - X₁.  Slope m = (21.6 -24.9) / (18 -7) = -3.3 / 11 = -0.3.
2. Each hour the candle height increases by -0.3 cm.  Alternately, it decreases in height by 0.3 cm.
3. Now you can plug in the point (14, Y_n)  into the equation for the line.  The equation for the line is Y2 - Y1 = m (X2-X1).  You can pick either of the known points on the line to substitute for Y1.  I'll pick (7, 24.9).  Substituting,  Yn - 24.9 = -0.3(14 - 7). 
4. Solve for Yn:
1. Yn = -0.3(14-7) + 24.9
2. Yn = 22.8
5. And just to show that you could have picked the other known point on the line,  let's see what happens if we had picked (18, 21.6)
1. Yn - 21.6 = -0.3(14 - 18)
2. Yn = -0.3(14-18) + 21.6
3. Yn = 1.2 + 21.6
4. Yn =  22.8   {same answer as above}

Answer 3

Calculate the rate of loss of height per hour:  (24.9 - 21.6) / (7 - 18). The answer here is negative, meaning no. of cm reduced per hour.  

 

Since the height is 24.9 at the earliest (7 hours) measurement, you just ADD 7 times the above change to 24.9, and you will get the height 7 hours later. Obviously it must be less than 24.9 cm but > 21.6.