Solve the Problem $P$ (In Decimal Form) at a Depth Of $x$

question 242

Multiple Choice

Solve the problem.
-Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light $P$ (in decimal form) at a depth of $x$ meters is given by $P = e ^ { - k x }$ , where $k$ is a constant related to the clarity and other physical properties of the water. The model for a particular lake is $P = e ^ { - 0.1284 x }$ . Determine the depth at which the light intensity is $80 \%$ of the value from the surface for this lake. Round to the nearest tenth of a meter.

• A) \(0.8 \mathrm {~m}\)
• B) \(34.1 \mathrm {~m}\)
• C) \(1.7 \mathrm {~m}\)
• D) \(16.2 \mathrm {~m}\)

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Definitions:

Absolute Threshold

The minimum intensity of a stimulus that one can detect 50% of the time, a basic concept in sensory psychology.

Inattentional Blindness

The phenomenon in which we shift our focus from one object to another and, in the process, fail to notice changes in objects to which we are not directly paying attention.

Motion Parallax

A depth cue involving the apparent relative motion of stationary objects as observed by an observer moving across the landscape.

Attentional Blindness

Also known as inattentional blindness, it is the phenomenon where an individual does not see new and unexpected changes in their visual field when their attention is focused elsewhere.