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).
Chapter6: Exponential And Logarithmic Functions
Section6.7: Exponential And Logarithmic Models
Problem 15TI: Cesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take...
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Transcribed Image Text: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).
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