Question

The intensky of light below the surface of a clear lake depends on many factors. One model thows that 19% of light is absorbed for each t-meter increvse.in depth. Find an exponential model, P, for the percentage of light that reaches a depth of of metes. P(d)= Uee your model to predict what percentage ef light will reach a depth of 9 meteis. (Round your answer to ene decimal place.)

Answer 1

An exponential decay model can be used to predict the percentage of light that reaches a certain depth in a clear lake. For a 19% light absorption per meter, the equation is P(d) = 100 * (0.81)^d. At a depth of 9 meters, approximately 14.1% of light remains.

Step-by-step explanation:

The intensity of light at a given depth in a clear lake can be modeled using an exponential decay function. In this case,

where we have a 19% absorption rate per meter, the function we'll use is of the form P(d) = 100 * (0.81)d, where P(d) is the percentage of light intensity at a depth d in meters, starting with 100% light at the surface.

Plugging the depth of 9 meters into the model to predict the percentage of light that will reach that depth, we get P(9) = 100 * (0.81)9 ≈ 14.1%.

Therefore, approximately 14.1% of the original light intensity will reach a depth of 9 meters in the lake.