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. IP = kl. Find the constant of proportionality k, where

An Introduction to Physical Science
14th Edition
ISBN:9781305079137
Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Chapter1: Measurement
Section: Chapter Questions
Problem 11E
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When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), wheret 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.
dI
Find the constant of proportionality k, where
dt
= kI.
k =
0.462
What is the intensity of the beam 18 feet below the surface? (Give your answer in terms of I. Round any constants or coefficients to five decimal places.)
0'
0.00024
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), wheret 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. dI Find the constant of proportionality k, where dt = kI. k = 0.462 What is the intensity of the beam 18 feet below the surface? (Give your answer in terms of I. Round any constants or coefficients to five decimal places.) 0' 0.00024
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