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 5 hours of burning, a candle has a height of 21.5 centimeters. After 21 hours of burning, its height is 16.7 centimeters. What is the height of the candle after 15 hours?

Answer 1

The height is 18.5cm

Explanation:

Given

Let

`y =height`

`x = time`

So, we have:

`(x_1,y_1) = (5,21.5)`

`(x_2,y_2) = (21,16.7)`

Required

The height after 15 hours

First, calculate the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

This gives:

`m = (16.7-21.5)/(21-5)`

`m = (-4.8)/(16)`

`m = -0.3`

The linear equation is then calculated as:

`y =m(x - x_1) + y_1`

Where

`m = -0.3`

`(x_1,y_1) = (5,21.5)`

This gives:

`y =-0.3(x - 5) + 21.5`

Open bracket

`y =-0.3x + 1.5 + 21.5`

`y =-0.3x + 23`

After 15 hours

`x = 15`

`y =-0.3*15 + 23`

`y =-4.5 + 23`

`y =18.5`

The height is 18.5cm