$6.()$ Consider an investment fund at $4\%$ annual interest $($compounded continuously$).$ It starts

at $$1$ million dollars and $$50,000$ are withdrawn every year $($you can assume the withdrawals are done

uniformly during the year$).$ Write a differential equation for the value of the fund y$($t$)($value in thousands

of dollars might be convenient$),$ solve the differential equation, and use the solution to determine how

long the fund will last.