Marine biology. The intensity of light entering water is reduced according to the exponential equation I = I 0 e − k d where I is the intensity d feet below the surface, I 0 is the intensity at the surface, and k is the coefficient of extinction. Measurements in the Sargasso Sea have indicated that half of the surface light reaches a depth of 73.6 feet. Find k (to five decimal places), and find the depth (to the nearest foot) at which 1% of the surface light remains.
Marine biology. The intensity of light entering water is reduced according to the exponential equation I = I 0 e − k d where I is the intensity d feet below the surface, I 0 is the intensity at the surface, and k is the coefficient of extinction. Measurements in the Sargasso Sea have indicated that half of the surface light reaches a depth of 73.6 feet. Find k (to five decimal places), and find the depth (to the nearest foot) at which 1% of the surface light remains.
Solution Summary: The author calculates the constant k and the depth at which 1% of the surface light remains, using the exponential equation for the intensity of light entering water.
Marine biology. The intensity of light entering water is reduced according to the exponential equation
I
=
I
0
e
−
k
d
where I is the intensity d feet below the surface, I0 is the intensity at the surface, and k is the coefficient of extinction. Measurements in the Sargasso Sea have indicated that half of the surface light reaches a depth of 73.6 feet. Find k (to five decimal places), and find the depth (to the nearest foot) at which 1% of the surface light remains.
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