Question

A 15-inch candle is lit and burns at a constant rate of 1.6 inches per hour.

a. The function f (t) = 15 - 1.6 t determines the length of the candle in inches given any number of hours t since the candle was lit. What does each part of the function definition represent?

Answer 1

c = 15: The height of candle is 15 inches when it is not lit.

m = -1.6: The height of candle decreases 1.6 inches for every hour it is lit.

Explanation:

We are given the following in the question:

Height of candle = 15 inches

`f (t) = 15 - 1.6 t`

This function gives the length of the candle in inches left after it was burn for t hours.

Comparing the given equation to a linear equation, we have:

`y = mx + c`

where m is the slope and c is the y-intercept.

Comparing we, get

m = -1.6 and c = 15

Interpretation:

c = 15 mean the y-intercept is 15 that is he value of function when t = 0, thus, the height of candle is 15 inches when it is not lit.

m = -1.6 is the rate of change of the function when t increases by 1 unit that is the height of candle decreases 1.6 inches for every hour it is lit.