After depositing an initial amount of $17,000 in an account that eams 7% 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 2800 - 400t 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.)
After depositing an initial amount of $17,000 in an account that eams 7% 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 2800 - 400t 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.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:After depositing an initial amount of $17,000 in an account that earns 7% 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 2800 – 400t
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.)
(a) The person contributed to the account for years before starting to withdraw from it.
(Simplify your answer.)
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