A 13-inch candle is lit and burns at a constant rate of 1.3 inches per hour. Let
t
represent the number of hours since the candle was lit, and suppose
f
is a function such that
f
(
t
)
represents the remaining length of the candle (in inches)
t
hours after it was lit.
why all those extra lines?
f(t) = 13 - 1.3t
To find the function that represents the remaining length of the candle, we need to consider the initial length of the candle and the burn rate.
Given:
- Initial length of the candle: 13 inches
- Burn rate: 1.3 inches per hour
We can assume that the remaining length of the candle is equal to the initial length minus the amount burned.
So, the function f(t) can be defined as:
f(t) = 13 - (burn rate * t)
Let's break down the steps to calculate the remaining length of the candle for a given time t:
1. Determine the burn rate:
- Given: Burn rate = 1.3 inches per hour
2. Calculate the remaining length of the candle for a given time t:
- f(t) = 13 - (burn rate * t)
That's it! You can now calculate the remaining length of the candle for any given time t using the function f(t).
To find the function f(t), we need to consider that the candle is burning at a constant rate of 1.3 inches per hour. So for each hour that passes, the candle burns 1.3 inches.
Initially, when the candle is lit, its length is 13 inches. As time passes, the length of the candle decreases by 1.3 inches for each hour that goes by.
Therefore, we can calculate the remaining length of the candle after t hours as:
f(t) = 13 - 1.3t
Where:
- f(t) represents the remaining length of the candle (in inches) after t hours.
- t represents the number of hours since the candle was lit.
- 13 is the initial length of the candle.
- 1.3t represents the amount the candle has burned after t hours.
So, for example, if two hours have passed since the candle was lit, we can calculate the remaining length of the candle as:
f(2) = 13 - 1.3(2) = 13 - 2.6 = 10.4 inches.