candle word problem

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
25.8
centimeters. After
26
hours of burning, its height is
18.6
centimeters. What is the height of the candle after
20
hours?

Answer 1

Height is a function of number of hours burned.

 

we have two points (t, h) where t is time as hours

burned and h is height.  Our points are

(8, 25.8), (26, 18.6).  Find slope:

m = (18.6-25.8)/(26-8) 

m = -7.2/18 = -0.4

 

h = mt  + b

h = -0.4t + b

 

we need to find the h intercept, b

which is candle height at time zero.

Plug in one of the points given:

25.8 = -0.4(8) + b

25.8 = -3.2 + b

b = 29 

 

Your equation is:

h = -0.4t + 29

 

After 20 hours we have

h = (-0.4)(20) + 29

h = 21 cm