Explanation Given: The number of gallons of brine in the tank is N o , the input flow rate of the brine is r i n and the output flow rate of the brine is r o u t and the concentration of the salt in the inflow is c i n . Procedure used: Rate of change of amount of salt with respect to time: d A d t = R i n − R o u t Here, the rate of change of amount of salt is d A d t , the inlet flow rate is R i n and the rate of output flow rate of salt is R o u t . Input flow rate of the salt: R i n = ( c o n c e n t r a t i o n o f s a l t i n inf l o w ) × ( i n p u t r a t e o f w a t e r ) Output flow rate of the salt: R o u t = ( c o n c e n t r a t i o n o f s a l t i n o u t l f o w ) × ( o u t p u t r a t e o f w a t e r ) Calculation: Write the expression for the rate of change of amount of salt with respect to time. d A d t = R i n − R o u t (1) Here, the rate of change of amount of salt is d A d t , the inlet flow rate is R i n and the rate of output flow rate of salt is R o u t . Write the expression for the input flow rate of the salt. R i n = ( concentration of salt in inflow ) × ( input rate of water ) (2) Write the expression for the output flow rate of the salt. R o u t = ( concentration of salt in outlfow ) × ( output rate of water ) (3) Substitute c i n lb / gal for ( concentration of salt in inflow ) and r i n gal / min for ( input rate of water ) in equation (2) R i n = ( concentration of salt in inflow ) × ( input rate of water ) R i n = c i n lb / gal × r i n gal / min R i n = c i n r i n lb / min Write the expression for number of gallons of brine left in the tank after t minutes

9th Edition

ISBN: 9781337810906

Author: ZILL

Publisher: CENGAGE L

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Chapter 1.3, Problem 12E

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The differential equation for the amount of salt A(t) in the tank at time t>0.

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The differential equation for the amount of salt A ( t ) in the tank at time t > 0 .

Solution Summary: The differential equation for the amount of salt A(t) in the tank at time t>0 is.

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The differential equation for the amount of salt A(t) in the tank at time t>0.

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The differential equation for the amount of salt A ( t ) in the tank at time t &gt; 0 .

Solution Summary: The differential equation for the amount of salt A(t) in the tank at time t>0 is.

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The differential equation for the amount of salt A(t) in the tank at time t>0.

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The differential equation for the amount of salt A ( t ) in the tank at time t > 0 .