When lit, a candle loses 5% of its original height every hour. Jennifer lit a candle with an original height of 8 inches.

Question

Please complete the following sentence by writing the number in the blank.

Until the candle has been burning for at least _______ hours, the height of Jennifer's candle will be more than 7 inches.

Answer 1

5% of its original height = 0.05*8 = 0.4 inches

So, every hour the candle's height reduces by 0.4 inches.

After 1 hour, the height will be 7.6 in. After 2 hours, it will be 7.2 in. After 3 hours, it will be 6.8, etc.

We need to find the time where the height will be 7 in. This is when the candle height has reduced by 1 in (from 8 in to 7 in). This will occur between 2 and 3 hours, as we can see from the above calculations. Specifically, the height will reduce by 1 inch after 1/0.4 = 2.5 hours.

Answer 2

7 > 8(0.95)^h

0.875 > 0.95^h

ln 0.875 > h ln 0.95

-0.1335 > -0.0513 h

2.60 > h

Answer 3

1hr=-.05*8"............................