When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), where t represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity of the incident beam. Find the constant of proportionality k, where = kl. dit k What is the intensity of the beam 13 feet below the surface? (Give your answer in terms of I- Round any constants or coefficients to five decimal places.)
When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), where t represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity of the incident beam. Find the constant of proportionality k, where = kl. dit k What is the intensity of the beam 13 feet below the surface? (Give your answer in terms of I- Round any constants or coefficients to five decimal places.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), where t represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial
intensity I of the incident beam.
Find the constant of proportionality k, where
dI
dt
k=
= KI.
What is the intensity of the beam 13 feet below the surface? (Give your answer in terms of I. Round any constants or coefficients to five decimal places.)
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