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 6 hours of burning, a candlehas a height of 21.4 centimeters. After 24 hours of burning, its height is 10.6 centimeters. What is the height of the candle after 10 hours?

Answer 1

A linear function implies that the equation governing the height of the candle h as a function of time t takes the form.

`h=mt+b`

we know that at t = 6, h = 21.4 and at t = 24, h = 10.6. From this we calculate the slope m:

`m=(10.6-21.4)/(24-6)=-0.6`

Now we find b from one of the data sets. Let us use t =6 , h= 21.4. plugging this into the first equation gives

`21.4=-0.6(6)+b`
`\therefore b=25`

Hence, the equation we sought after is

`h=-0.6t+25`

Now it's easy to calculate the height after 10 hours - we simply put in t = 10.

`h=-0.6(10)+25`
`\textcolor{#FF7968}{h=19.}`

Hence, the height after 10 hours is 19 centimetres.