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Enter an equation for the function. Give your answer in the form a(6"). In theevent that a = 1, give your answer in the form b".A laser beam with an output of 4 milliwatts is directed into a series of mirrorsThe laser beam loses 6% of its power every time it reflects off of a mirror. Thepower p(n) is a function of the number n of reflections.The equation is p(n) = 0

Enter An Equation For The Function Give Your Answer In The Form A6 In Theevent That A 1 Give Your Answer In The Form BA Laser Beam With An Output Of 4 Milliwatt class=

Sagot :

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]

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