Answer:
[tex] L = -1.5 \frac{in}{hr} t + 11.2[/tex]
Step-by-step explanation:
For this case we need to define some notation:
[tex] L[/tex] represent the remaining length of the candle in inches
[tex] t[/tex] 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: [tex] L =f(t)[/tex] L is a function of t.
And for this case we have a constant rate given of:
[tex] m = \frac{\Delta L}{\Delta t}= -1.5 \frac{in}{hr}[/tex]
And we know a initial condition [tex] L(2) = 8.2 in[/tex]
So then since we have a constant rate of change we can use a linear model given by:
[tex] L = m t +b[/tex]
Where m is given and we need to find b. If we use the initial condition we have this:
[tex] 8.2 = -1.5 \frac{in}{hr} (2) +b[/tex]
And solving for b we got:
[tex] b = 8.2 +1.5*2=11.2 in[/tex]
So then our lineal model would be given by:
[tex] L = -1.5 \frac{in}{hr} t + 11.2[/tex]
The remaining length of the candle in inches, L after t hours is given by L = -1.5t + 11.2
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let L represent the length of the candle in hours after t hours.
The length of the candle changes at a constant rate of -1.5 inches per hour. hence:
2 hours after the candle was lit the candle is 8.2 inches long. Hence:
Hence:
L = -1.5t + 11.2
The remaining length of the candle in inches, L after t hours is given by L = -1.5t + 11.2
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