Question

A 11-inch candle is lit and burns at a constant rate of 0.9 inches per hour. Let t t represent the number of hours since the candle was lit, and suppose f f is a function such that f ( t ) f(t) represents the remaining length of the candle (in inches) t t hours after it was lit. Write a function formula for f f.

Answer 1

Answer: F(t) = 11 - 0.9(t)

Explanation:

We know the following:

The candle burns at a ratio given by:

Burning Ratio (Br)  = 0.9 inches / hour

The candle is 11 inches long.

To be able to create a function that give us how much on the candle remains after turning it after a time (t). We will need to know how much of the candle have been burned after t.

Let look the following equation:

Br = Candle Inches (D) / Time for the Candle to burn (T)      (1)

Where (1) is similar to the Velocity equation:

Velocity (V) = Distance (D)/Time(T)

This because is only a relation between a magnitude and time.

Let search for D on (1)

D = Br*T  (2)

Where D is how much candle has been burn in a specif time

To create a function that will tell us how longer remains of the candle after be given a variable time (t) we use the total lenght minus (2):

How much candle remains? ( F(t) ) = 11 inches - Br*t

F(t) = 11 - 0.9(t)

F(t) defines the remaining length of the candle t hours after being lit