A person is depositing money into a bank account continuously at the rate of $5,000 per year, and the account earns interest of 5% annually compounded continuously, that is, the amount increases constantly at a rate of 5% the current amount. (a) If y(t) represents the amount of money in the account at time t (measured in years), explain why y satisfies the equation y = 0.05y + 5000 (b) Find the general solution to the differential equation. (c) The person began its first year with $10,000. Find the amount of money in the account after 4 years. (You don't need to give the answer as a decimal number, just finding the mathematical expression is enough).

A person is depositing money into a bank account continuously at the rate of $5,000 per year, and the account earns interest of 5% annually compounded continuously, that is, the amount increases constantly at a rate of 5% the current amount. (a) If y(t) represents the amount of money in the account at time t (measured in years), explain why y satisfies the equation y = 0.05y + 5000 (b) Find the general solution to the differential equation. (c) The person began its first year with $10,000. Find the amount of money in the account after 4 years. (You don't need to give the answer as a decimal number, just finding the mathematical expression is enough).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.EA: Extended Application Managing Renewable Resources

Problem 2EA

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