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:

Parasympathetic Nervous System

Part of the autonomic nervous system that promotes relaxation, digestion, and nutrient absorption, counterbalancing the sympathetic nervous system.

Parasympathetic Nervous System

The part of the autonomic nervous system responsible for conserving energy and promoting rest and digest functions, often termed as the "rest and digest" system.

Stimulates Digestion

Refers to factors or substances that enhance the process of breaking down food into absorbable nutrients within the digestive system.

Slows Heartbeat

A decrease in heart rate, which can be influenced by various factors such as relaxation techniques, medications, or physical fitness levels.