Suppose you contribute $15,000 per year into your retirement fund at work by making small deposits throughout the year. The fund grows at a rate of 6.2% per year compounded continuously. After 30 years you retire and begin to withdraw from the fund at a rate of $4,500 per month. If you do not make any additional deposits after retirement, how long will your money last? Solve this problem in two steps one D.E. should represent the situation before retirement and the 2nd D.E. should represent the situation after retirement. You should have two first-order linear differential equations that are solved via the integrating factor method. Finally, provide a graph reflecting the change in the amount contained in the fund from inception to depletion. Suppose you contribute $15,000 per year into your retirement fund at work by making small deposits throughout the year. The fund grows at a rate of 6.2% per year compounded continuously. After 30 years you retire and begin to withdraw from the fund at a rate of $4,500 per month. If you do not make any additional deposits after retirement, how long will your money last? Solve this problem in two steps one D.E. should represent the situation before retirement and the 2nd D.E. should represent the situation after retirement. You should have two first-order linear differential equations that are solved via the integrating factor method. Finally, provide a graph reflecting the change in the amount contained in the fund from inception to depletion