According to the Bouguer-Lambert law, a beam of light that strikes the surface of a body of water with intensity I will have intensity I at a depth of x meters, where the constant k, called the absorption coefficient, depends on such things as the wavelength of the beam of light and the purity of the water. Suppose a given beam of light is only 5% as intense at a depth of 2 meters as it is at the surface. Find k and determine at what depth (to the nearest meter) the intensity is 1% of the intensity at the surface. (This explains why plant life exists only in the top 10 m of a lake or sea
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