Explanation Given: Initial amount of chemical is 5 grams and the initial volume of solution is 100 liters. Alcohol entering rate is 2 liter per minute and solution outgoing rate is 1 liter per minute. Calculation: Let at any time t (in minute) the amount of chemical in the mixture is y. Then rate of change is amount of chemical is d y d t is equal to the difference of the rate of chemical in and rate of chemical out. Rate of chemical in is equal to zero because pure alcohol is entering. And rate of chemical out is equal to y V ( 1 gal per minute ) where V is volume of mixture at any time t. Then d y d t = − y V Change in volume is equal to the difference of liquid in and liquid out. d V d t = ( 2 − 1 ) d V d t = 1 Integrate both sides with respect to t. ∫ d V = ∫ d t V = t + C Initially the volume of mixture is 100 liters 100 = 0 + C C = 100 Then the volume at any time t is V = t + 100 Now, d y d t = − y t + 100 Integrate both sides with respect to t To determine (b) To find: The amount of chemical in mixture after 30 minutes.

Student's Solutions Manual for Calculus for the Life Sciences (2nd Edition)

2nd Edition

ISBN: 9780321963833

Author: Raymond N. Greenwell; Nathan P. Ritchey; Margaret L. Lial

Publisher: PEARSON

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Chapter 11.6, Problem 14E

To determine

(a)

To find:

The equation of amount of chemical in the solution at any time t.

To determine

(b)

To find:

The amount of chemical in mixture after 30 minutes.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.6, Problem 13E

Chapter 11.6, Problem 15E

Chapter 11 Solutions

Student's Solutions Manual for Calculus for the Life Sciences (2nd Edition)

Ch. 11.1 - YOUR TURN 1 Find all solutions of the differential...Ch. 11.1 - Prob. 2YT Ch. 11.1 - Prob. 3YT Ch. 11.1 - YOUR TURN In Example 6, find the goat population...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 2E Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

(a) To find: The equation of amount of chemical in the solution at any time t .

Solution Summary: The author explains the equation of amount of chemical in the solution at any time t.

Concept explainers

Videos

(a)

To find:

The equation of amount of chemical in the solution at any time t.

(b)

To find:

The amount of chemical in mixture after 30 minutes.

Want to see the full answer?

Chapter 11 Solutions

(a) To find: The equation of amount of chemical in the solution at any time t .

Solution Summary: The author explains the equation of amount of chemical in the solution at any time t.

Concept explainers

Videos

(a) To find: The equation of amount of chemical in the solution at any time t.

(b) To find: The amount of chemical in mixture after 30 minutes.

Want to see the full answer?

Chapter 11 Solutions

(a)

To find:

The equation of amount of chemical in the solution at any time t.

(b)

To find:

The amount of chemical in mixture after 30 minutes.