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 candlehas a height of 24.5 centimeters. After 18 hours of burning, its height is 20.6 centimeters. What is the height of the candle after 8 hours?

Answer 1

23.6 centimeters

Step-by-step explanation

The height of the candle is a linear function of time it has been burning.

A linear function is generally represented as:

y = mx + c

where m = slope

c = y intercept

From the equation:

y = height of candle

x = time it has been burning

After 5 hours, it's height was 24.5 cm

After 18 hours, it's height is 20.6 cm

We have to find the function that represents the height of the candle.

We will first find the slope and then use formula:

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

Find the slope by using formula:

`\begin{gathered} m\text{ = }(y_2-y_1)/(x_2-x_1) \\ \text{where (x1, y1) = (5, 24.5)} \\ (x2,\text{ y2) = (18, 20.6)} \\ \Rightarrow\text{ m = }\frac{20.6\text{ - 24.5}}{18\text{ - 5}}\text{ = }(-3.9)/(13) \\ m\text{ = }-0.3 \end{gathered}`

Now, find the function:

`\begin{gathered} y\text{ - 24.5 = -0.3(x - 5)} \\ y\text{ - 24.5 = -0.3x + 1.5} \\ y\text{ = -0.3x + 1.5 + 24.5} \\ \Rightarrow\text{ y = -0.3x + 26} \end{gathered}`

Now, to find the height of the candle after 8 hours, we will make x = 8 and then find y:

y = -0.3(8) + 26

y = -2.4 + 26

y = 23.6 centimeters

That is the height of the candle after 8 hours.