What is the height of the candle after 14 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 24.2 centimeters. After 20 hours of burning, its height is 17 centimeters. What is the height of the candle after 14 hours?

Answer 1

Determine rate of change

(17 - 24.2) / (20 - 8)

-7.2 / 12

Height = 24.2 + (-7.2 / 12)(6) measuring 6 hours

Can you calculate and answer?

Answer 2

As it is given that the height of the candle is linear to the amount of time. Now, let's the time be on the x- axis and the y- axis be the height of the candle. then the slop of the linear relationship represent as,

Point 1 of the slop (x_1, y₁ ) =(8, 24.2)

Point 2 of the slop (x₂, y₂) =( 20,17)

slop can be written as

m=y2-y1/x2-x1

17-24.2/20-8

m= -.6

Now the equation of the linear eq. can be written as

y=mx+b

y1= mx1+b

24.2 =(-.4 *8) +b

24.2= -3.2+b

b= 27

Now, In order to calculate the height of the candle after 14 hour we will plug the value of the x as 14

y= -.6x+27

y= -.6(14) +27

y= -8.4+27

y=18.6 is the height of candle after 14 hour