Question

A candle is lit and burns and the length of the candle changes at a constant rate of -1.5 inches per hour. 2 hours after the candle was lit the candle is 8.2 inches long.
Write a formula that expresses the remaining length of the candle in inches, L, in terms of the number of hours t that have elapsed since the candle was lit.

Answer 1

Answer:

$L = -1.5 \frac{in}{hr} t + 11.2$

Step-by-step explanation:

For this case we need to define some notation:

$L$ represent the remaining length of the candle in inches

$t$ represent the time in hours that have elapsed since the candle was lit.

For this case we assume that L and f are related so then we can write this like that: $L =f(t)$ L is a function of t.

And for this case we have a constant rate given of:

$m = \frac{\Delta L}{\Delta t}= -1.5 \frac{in}{hr}$

And we know a initial condition $L(2) = 8.2 in$

So then since we have a constant rate of change we can use a linear model given by:

$L = m t +b$

Where m is given and we need to find b. If we use the initial condition we have this:

$8.2 = -1.5 \frac{in}{hr} (2) +b$

And solving for b we got:

$b = 8.2 +1.5*2=11.2 in$

So then our lineal model would be given by:

$L = -1.5 \frac{in}{hr} t + 11.2$