Question

A candle burned at a steady rate. After 33 minutes, the candle was 11.2 inches tall. Eighteen minutes later, it was 10.75 inches tall. Use an equation in point-slope form to determine the height of the candle after 2 hours. Round the answer to the tenth place if necessary

Answer 1

9.025 inches

Explanation:

Let the length be represented by:

`L = mt+L_0`

Where
`L` is the length of candle at time
`t`

`m` is the rate at which the candle is burning.

And
`L_0` is the initial length of the candle.

As per the question statement, let us put the given values in the equation.

`11.2 = m* 33 + L_0 .... (1)\\10.75 = m* 51+L_0 ..... (2)`

Subtracting (1) from (2):

`0.45 = -18m\\\Rightarrow m = -0.025`

Putting the value of
`m` in the equation (1):

`11.2 = -0.025 * 33+L_0\\\Rightarrow L_0 = 12.025`

Therefore, the equation becomes:

`L = -0.025t + 12.025`

Now, we have to find the height of candle after 2 hours.

2 hours mean 120 minutes.

`L = -0.025 * 120 + 12.025\\\Rightarrow L = 9.025\ inches`

Therefore, the height of candle is 9.025 inches.