Question

The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives with a slope of -0.6. See the figure below. Suppose that the height of the candle after 11 hours is 22.4 centi meters. What was the height of the candle after 8 hours?

Answer 1

We can model the candle's height using the linear function:

`h=mt+b`

Where

h is the height

m is the slope

t is the time

b is the y-intercept

Given slope = -0.6, we can write:

`h=-0.6t+b`

Also given, at t = 11 hours, the height, h, is 22.4 cm. Thus, we can find b:

`\begin{gathered} h=-0.6t+b \\ 22.4=-0.6(11)+b \\ 22.4=-6.6+b \\ b=22.4+6.6 \\ b=29 \end{gathered}`

The equation of the candle's height:

`h=-0.6t+29`

We want to find height of candle after 8 hrs, so we put 8 into "t" of the equation and find the corresponding "h". Shown below:

`\begin{gathered} h=-0.6t+29 \\ h=-0.6(8)+29 \\ h=24.2 \end{gathered}`

The height, after 8 hrs, was 24.2 centimeters.