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A large tank s filled to capacity with 400 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds of salt in the tank at time t.. A(t) = lb

A large tank s filled to capacity with 400 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds of salt in the tank at time t.. A(t) = lb

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A large tank is filled to capacity with 400 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds of salt in the tank at time t. A(t) = [Box for answer] lb
Transcribed Image Text:A large tank is filled to capacity with 400 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds of salt in the tank at time t. A(t) = [Box for answer] lb
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 25.3% of the initial intensity \( I_0 \) of the incident beam. What is the intensity of the beam 11 feet below the surface? (Give your answer in terms of \( I_0 \). Round any constants or coefficients to five decimal places.)
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 25.3% of the initial intensity \( I_0 \) of the incident beam. What is the intensity of the beam 11 feet below the surface? (Give your answer in terms of \( I_0 \). Round any constants or coefficients to five decimal places.)
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According to bartleby guidelines we are supposed to do the first one of multiple questions

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Suppose A( t ) is the amount of salt at any time t 

As we know that 

Rate of change of amount of salt at any time t is given as 

fraction numerator d A over denominator d t end fraction space equals space r a t e space o f space s a l t space i n f l o w space minus space r a t e space o f space s a l t space o u t f l o w space

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