From the data provided, we have the following;
Initial power output = 4 milliwatts
Power lost per reflection = 6% (OR 0.06)
We need to find a function that shows the power each time the laser beam is reflected off a mirror.
Note that the general equation for an exponential decay/loss is given as;
[tex]\begin{gathered} y=a(1-r)^x \\ OR \\ f(x)=a(1-r)^x \end{gathered}[/tex]
Note also that (1 - r) is often replaced by b. Therefore, the equation can be written as;
[tex]\begin{gathered} f(x)=a(1-r)^x^{} \\ f(x)=ab^x \end{gathered}[/tex]
Where the number of reflections is given by n and p(n) is a function of the number of reflections, we now have;
[tex]p(n)=ab^n[/tex]
Where the variables are;
[tex]\begin{gathered} a=4\text{ milliwatts (initial value)} \\ r=0.06 \end{gathered}[/tex]
We now have the function as;
[tex]\begin{gathered} p(n)=a(1-0.06)^n \\ p(n)=a(0.94)^n \end{gathered}[/tex]
ANSWER:
[tex]p(n)=a(0.94)^n[/tex]
