Simplify.
1 answer:
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Answer: The equation is f(x) = ;
The piece of plastic has to have 10mm of thickness.
Step-by-step explanation: It is known that with 1 mm of thickness, 5% of the intensity is reduced. So, 95% of the light is transmitted.
For each milimetre added, "more" 95% of light is transmitted.
For example, if another milimetre of plastic is added, another 0.95 of light is transmitted:
0.95.0.95 = 0.9025 of light reach the visor
So, the model that relate thickness of plastic and intensity of light is:
f(x) =
in which:
f(x) is the intensity of light;
x is thickness in mm;
Using the equation, the thickness necessary to reduce intensity to 60% is:
f(x) =
0.6 =
log 0.6 = log
x. log (0.95) = log (0.6)
x =
x = 9.95
x ≈ 10
The thickness necessary to reduce intensity of light to 60% is 10mm.