Explanation Formula used: If money is continuously withdrawn from the account at the rate of $ m per year, then A satisfies the equation d A d t − r A = − m ; where A ( 0 ) = P where d A d t is the rate of change of the amount A , rA is the rate of growth from continuous compounding and m is the rate of withdrawal. Integrating factor: The integrating factor of the First-Order linear differential equation y ′ + f ( x ) y = g ( x ) is I ( x ) = e ∫ f ( x ) d x . Calculation: It is given that the initial amount deposited is $60,000 into an account at a rate of 5% which is compounded continuously and then money is continuously drawn at a constant rate of $5,000 a year until the account is depleted. Then, substitute r = 0.05 , m = 5 , 000 and P = 60 , 000 in the above equation. Therefore, the amount A at any time t must satisfy the equation d A d t − 0.05 A = − 5 , 000 ; A ( 0 ) = 60 , 000 . Now find the integrating factor. I ( t ) = e ∫ − 0.05 d t = e − 0.05 t Multiply both sides of the standard form by the integrating factor. e − 0.05 t d A d t − 0.05 e − 0.05 t A = − 5 , 000 e − 0.05 t ( A e − 0.05 t ) ′ = − 5 , 000 e − 0.05 t [ ∵ ( x y ) ′ = x y ′ + x ′ y ] Integrating on both sides, ∫ ( A e − 0.05 t ) ′ d t = ∫ − 5 , 000 e − 0

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

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 9, Problem 43RE

To determine

To find: The amount in the account at time t, the value of t at which the amount becomes $0 and the total amount withdrawn from the account.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 42RE

Chapter 9, Problem 44RE

Students have asked these similar questions

i attached the question and the way i solved it, i believe i made an error, could you point it out for me because the correct answer is 3pi/2correct answer is D, please see both attached photos

Question 3 and 4

could you explain this using stoke theoremi already circled the correct answer

Chapter 9 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

Ch. 9.1 - Show that y=Cx+1 is the general solution of the...Ch. 9.1 - Prob. 2MP Ch. 9.1 - Prob. 3MP Ch. 9.1 - Prob. 4MP Ch. 9.1 - Prob. 5MP Ch. 9.1 - Prob. 1ED Ch. 9.1 - Prob. 2ED Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E

Knowledge Booster

Learn more about

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

The amount in the account at time t , the value of t at which the amount becomes $0 and the total amount withdrawn from the account.

Solution Summary: The author calculates the integrating factor of the First-Order linear differential equation.

Concept explainers

Videos

To find: The amount in the account at time t, the value of t at which the amount becomes $0 and the total amount withdrawn from the account.

Want to see the full answer?

Chapter 9 Solutions