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Math Calculus Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)

In Exercises 21 − 25 , solving the differential equations that arise from modeling may require using integration by parts. [See formula ( 1 ) ]. A Savings Account with Withdrawals After depositing an initial amount of $ 10 , 000 in a savings account that earns 4 % interest compounded continuously, a person continued to make deposits for a certain period of time and then started to make withdrawals from the account. The annual rate of deposits was given by 3000 − 500 t dollars per year, t years from the time the account was opened. (Here, negative rates of deposits correspond to withdrawals.) a. How many years did the person contribute to the account before starting to withdraw money from it? b. Let P ( t ) denote the amount of money in the account, t years after the initial deposit. Find an initial-value problem satisfied by P ( t ) . (Assume that the deposits and withdrawals were made continuously.

In Exercises 21 − 25 , solving the differential equations that arise from modeling may require using integration by parts. [See formula ( 1 ) ]. A Savings Account with Withdrawals After depositing an initial amount of $ 10 , 000 in a savings account that earns 4 % interest compounded continuously, a person continued to make deposits for a certain period of time and then started to make withdrawals from the account. The annual rate of deposits was given by 3000 − 500 t dollars per year, t years from the time the account was opened. (Here, negative rates of deposits correspond to withdrawals.) a. How many years did the person contribute to the account before starting to withdraw money from it? b. Let P ( t ) denote the amount of money in the account, t years after the initial deposit. Find an initial-value problem satisfied by P ( t ) . (Assume that the deposits and withdrawals were made continuously.

Solution Summary: The author explains how the person contributed 6 years before withdrawing from a savings account. The differential equation is satisfied by P(t).

Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)

Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)

15th Edition

ISBN: 9780137590728

Author: Larry Goldstein, David Lay

Publisher: PEARSON+

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Differential Equations

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Textbook Question

Chapter 10.4, Problem 23E

In Exercises 21 − 25 , solving the differential equations that arise from modeling may require using integration by parts. [See formula ( 1 ) ].

A Savings Account with Withdrawals After depositing an initial amount of $ 10 , 000 in a savings account that earns 4 % interest compounded continuously, a person continued to make deposits for a certain period of time and then started to make withdrawals from the account. The annual rate of deposits was given by 3000 − 500 t dollars per year, t years from the time the account was opened. (Here, negative rates of deposits correspond to withdrawals.)

a. How many years did the person contribute to the account before starting to withdraw money from it?

b. Let P ( t ) denote the amount of money in the account, t years after the initial deposit. Find an initial-value problem satisfied by P ( t ) . (Assume that the deposits and withdrawals were made continuously.

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Chapter 10.4, Problem 22E

Chapter 10.4, Problem 24E

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Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)

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