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 12 hours of burning, a candle has a height of 19.8 centimeters. After 27 hours of burning, its height is 18.3 centimeters. What is the height of the candle after 22 hours?

Answer 1

Answer: The height of candle becomes 18.8 cm after 22 hours.

Step-by-step explanation:

Since we have given that

After 12 hours of burning, a candle has a height of 19.8 centimeters.

and

After 27 hours of burning, its height is 18.3 centimeters.

Let x coordinate represents the number of hours and y coordinate represents the height.

So, we have (12,19.8) and (27,18.3)

So, the equation of line becomes,

$y-y_0=\dfrac{y_1-y_0}{x_1-x_0}(x-x_0)\\\\y-19.8=\dfrac{18.3-19.8}{27-12}(x-12)\\\\y-19.8=\dfrac{-1.5}{15}(x-12)\\\\y-19.8=-0.1(x-12)\\\\y-19.8=-0.1x+1.2\\\\y+0.1x-19.8-1.2=0\\\\y+0.1x-21=0\\\\y=21-0.1x$

So, After 22 hours, height of the candle becomes,

$y=-0.1\times 22+21=18.8\ cm$

Hence, the height of candle becomes 18.8 cm after 22 hours.