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Answer :
The value of k at this location is 10.
To find the value of k at the given location, we use the provided information about the intensity of light at the surface and at a certain depth below the surface. Using the formula for intensity of light, I = I0 * e^(-kx), where I0 is the intensity at the surface and x is the distance below the surface, we substitute the given values into the equation. With the intensity at the surface (100 lumens) and 5 meters below the surface (50 lumens), we can solve for k. By rearranging the equation and isolating k, we find that k = ln(I0/I) / x. Substituting the given values, we calculate k to be 10, indicating the clarity of the water at this location.
By substituting the given values of intensity at the surface and at 5 meters below the surface into the formula for intensity of light, we can determine the value of k. This value of k represents the rate at which the intensity of light decreases with depth in the water. The clarity of the water affects the value of k, with clearer water having lower values of k and less attenuation of light with depth.
The calculated value of k provides insight into the clarity of the water at the specified location. A higher value of k indicates greater attenuation of light with depth, suggesting poorer water clarity, while a lower value of k indicates clearer water with less attenuation of light.
Therefore, at this location, the value of k is determined to be 10, reflecting the clarity of the water and its effect on the intensity of light at different depths below the surface.
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