Chapter 6, Problem 12PS

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Use the solution of the differential equation in Exercise 11 and the given values to find the concentration C as a function of time t, and use a graphing utility to graph the function.(a) V = 2 liters R = 0.5 liter per minute C 0 = 0.6 mole per liter(b) V = 2 liters R = 1.5 liters per minute C 0 = 0.6 mole per liter

(a)

To determine

To graph: The concentration function C as obtained by V=2 liters,  R=0.5 litre per minute and C0=0.6 mole per litre also graph the function with the use of graphing utility.

Explanation

Given:

The provided differential equation is,

dCdt=(âˆ’RV)C

where C=C0 at t=0

The provided values are

V=2Â litersR=0.5Â litreÂ perÂ minuteC0=0.6Â moleÂ perÂ litre

Graph:

Consider the provided equation,

dCdt=(âˆ’RV)C

The solution to this differential equation is,

â€‰â€‰â€‰dCdt=(âˆ’RV)Câ€‰â€‰â€‰dCC=âˆ’RVdtâˆ«dCC=âˆ’âˆ«RVdtâ€‰â€‰lnC=âˆ’RVt

(b)

To determine

To graph: The concentration function C as obtained by the provided values.

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