(Solved): Please answer a, b, and C Please answe a,b, and c A person is depositing money into a bank account c ...

A person is depositing money into a bank account continuously at the rate of \( \$ 5,000 \) per year, and the account earns interest of \( 5 \% \) anmually 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 \( t \) (mesusured itt yeare), explain why \( y \) satisfies the equation \[ y^{\prime}=0.05 y+5000 \] (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 \[ y^{\prime}=0.05 y+5000 \] (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).