   Chapter 2.6, Problem 68E

Chapter
Section
Textbook Problem

(a) A tank contains 5000 L of pure water. Brine that contains 30 g of salt per liter of water is pumped into the tank at a rate of 25 L/min. Show that the concentration of salt after t minutes (in grams per liter) is c ( t ) = 30 t 200 + t (b) What happens to the concentration as t → ∞?

(a)

To determine

To show: The concentration of salt after t minutes is C(t)=30t200+t.

Explanation

Proof:

The volume of the tank is 5000L initially.

The volume of the tank increases by 25L per minute

Therefore, the volume of the tank at time t is 5000+25t .

Concentration of brine in water which is entering tank is 30g per Litre.

The water is entering the tank at a rate of 25L per minute.

The amount of salt entering the tank is 30×25=750 grams per minute.

Therefore, the amount of salt in the tank after t minutes is 750t.

Concentration of the salt after time t=Amount of saltVolume o

(b)

To determine

To find: The value of concentration of the salt after t minutes when t approaches infinity.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Solve the equations in Exercises 112 for x (mentally, if possible). 3x+1=x

Finite Mathematics and Applied Calculus (MindTap Course List)

Factoring Trinomials Factor the trinomial. 72. 6y2 + 11y 21

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 3540, rationalize the numerator of each expression. 40. x+3x3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In Problems 13-24, find the indicated derivative. 24. Find if

Mathematical Applications for the Management, Life, and Social Sciences

For y = f (u) and u = g(x), dydx=dydududx.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

How does a full-text database differ from other databases?

Research Methods for the Behavioral Sciences (MindTap Course List) 