What is the height of the candle after 30 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
15
hours of burning, a candle has a height of
12
centimeters. After
33
hours of burning, its height is
1.2
centimeters.

Answer 1

This is a linear equation.

y = mx + b

The slope (m) is rate, with units of y-units per x-unit.

 

We know two (x,y) points:

(15, 12) and (33, 1.2)

 

m = (1.2 - 12) / (33 - 15) = -10.8 /18 = -0.6 cm/hr

 

Now that you know the slope, you could find the intercept (b) with the point-slope equation, or by substituting a know x, y, and m into y=mx+b, then solving for b.

 

Or you can just calculate how much it burned down from 12 cm between the 15th and 30th hour.  In those 15 hours, it would have shortened by (15)(m) cm.

(15)(0.6) = 9 cm

 

12 -9 = 3 cm