1. The problem statement, all variables and given/known data a. Assume that yo dollars are deposited into an account paying r percent compounded continuously. If withdrawals are at an annual rate of 200t dollars (assume these are continuous), find the amount in the account after T years. b. Consider the special case if r = 10% and y0=$20000 c. When will the account be depleted if y0=$5000? Give your answer to the nearest month. 2. Relevant equations 3. The attempt at a solution I've realized that the rate at which the account balance varies is the following: dy/dt = ry - 200 (where r is the r percent rate, 0.10; and y the amount of money present) However, when i try to obtain the differential equation, I keep getting that the amount of money present is the following: y(T) = 200/r + (y0-200/r)erT This would, mean that the function would never decrease in the case of $20000 and as well for $5000 (meaning it will never be depleted). However, I'm pretty sure that i'm wrong on this one. Could anyone please help me with this? My procedure: 1/(ry-200) dy = 1 dt (integrate both parts) ln(ry-200) 1/r = t + M1 ln(ry-200) = rt + M2 M3ert=ry-200 y = M4ert + 200/r Then, if y(0) = y0: y0 - 200/r = M4 We then plug this result into our equation: y = 200/r + (y0 - 200/r)erT This corresponds to the equation i've been getting. Is my procedure done right?