MHB Find Glass Thickness to Block 25% of Light in Sunglasses

AI Thread Summary
To determine the glass thickness needed to block 25% of light in sunglasses, the equation I(x) = I0 (0.8)^x is used, where I0 is the initial light intensity. Setting the equation to 75% of I0 leads to the equation 0.75 I0 = I0 (0.8)^x. Solving for x involves understanding logarithmic and exponential relationships. The discussion emphasizes the importance of logarithms in solving such equations. Ultimately, the focus is on finding the appropriate thickness of the glass to achieve the desired light blockage.
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The intensity, I of light in lumens, passing through the glass of a pair of sunglasses is given by the
equation I(x) = I0 (0.8)^x , where x is the thickness of the glass in millimetres and I0 is the intensity of
light entering the glasses. How thick should the glass be so that it will block 25% of the light entering
the sunglasses?
 
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fxacx said:
The intensity, I of light in lumens, passing through the glass of a pair of sunglasses is given by the
equation I(x) = I0 (0.8)^x , where x is the thickness of the glass in millimetres and I0 is the intensity of
light entering the glasses. How thick should the glass be so that it will block 25% of the light entering
the sunglasses?

$0.75 I_0 = I_0 (0.8)^x$

solve for x ...
 
So the question is, again, do you know how to solve $a^x= y$? You titled this "Log/exponential word problem". Do you know what "logarithms" and "exponentials" are and how they are related?
 
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