We want to know the height of a candle after 16 hours.
We know that the height is a linear function of the amount of time (in hours) it has been burning. This means that we can write it as:
[tex]f(x)[/tex]where x represents the number of hours burning.
Also, we have that after 10 hours of burning, the candle has a height of 17 centimeters, which means that we can write it as a point of the function:
And after 23 hours of burning its height is 11.8 centimeters, so we can write the second point of the function will be:
[tex](23,11.8)[/tex]We will find the linear function that describes the height. Using the two points, we will find the slope and the y-intercept.
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{11.8-17}{23-10}=\frac{-5.2}{13}=-0.4[/tex]And for the y-intercept, we replace a point on the slope-intercept form, and we clear out the y-intercept.
[tex]\begin{gathered} y=mx+b \\ 17=-0.4(10)+b \\ 17=-4+b \\ 17+4=b \\ 21=b \end{gathered}[/tex]This means that the y-intercept is 21, and the linear function that describes the height is given by:
[tex]y=-0.4x+21[/tex]For finding the height of the candle after 16 hours, we replace x by 16, and we obtain:
[tex]\begin{gathered} y=-0.4(16)+21 \\ =-6.4+21 \\ =14.6 \end{gathered}[/tex]This means that the height of the candle after 16 hours is 14.6 centimeters.
