Question

The intensity i of a light a distance x meters beneath the surface of a lake decreases exponentially. if the light intensity at 6 meters is 70% of the intensity at the surface, at what depth (in m) will the intensity be 55%? (round your answer to the nearest meter.)

Answer 1

The intensity of light decreases exponentially beneath the surface of a lake. The depth at which the intensity is 55% can be found using the inverse square law and the given information. The depth is approximately 8 meters.

Step-by-step explanation:

The intensity of light decreases exponentially as it travels beneath the surface of a lake. According to the inverse square law, when the distance is doubled, the intensity decreases to one-fourth of the original intensity.

In this case, the light intensity at 6 meters is 70% of the intensity at the surface. To find the depth at which the intensity is 55%, we can set up the following equation:

0.55 = (0.7) * (1/4)^(x/6)

Solving this equation, we find that x is approximately 8 meters.