Answer to Question #134455 in Algebra for joseph Se

Question

The percent of light that will pass through a material is given by the formula log P = −kd, where P is the percent of light passing through the material, k is a constant that depends on the material, and d is the thickness of the material in centimeters.

The constant k for a piece of tinted glass is 0.6. How thick is a piece of this glass that allows 55% of the light incident to the glass to pass through it? Round to the nearest hundredth of a centimeter.

Answer 1

Consider the equation log(P)=-k*d, where where P is the percentage of light passing through the material, k is a constant that depends on the material, and d is the thickness of the material in centimeters. The constant k for a piece of tinted glass is 0.6, and P is equal to 55%. Substitute the values in the formula and get the following equation with the unknown d: log(0.55)=-0.6*d. Divide both parts of the equation by (-0.6) and get: (-10/6)*log(0.55)=d. Thus, the approximate value of d=1 cm.