1. The problem statement, all variables and given/known data Oil is released from a submerged source at a constant flow of rate of Q=(0.1 m3)/s. Density of oil (p=870 kg/m3) is less than that of water and since oil is only sparingly soluble in water a slick will form on the water surface. Once its formed it will have a tendency to spread as more oil is added but also have a tendency to shrink as the oil both evaporates to the air and dissolves in the water. Eventually it would reach a constant size when these two tendencies became balanced. A mass balance on the slick provides the following relationship: dM/dt = rate of oil slick from the source - rate of dissolution - rate of evaporation where each term is in kg/s and where M is the mass of the slick. For this particular oil the rate of dissolution per square meter is 0.0000011 kg/m2s and the rate of evaporation per square meter is 0.004 kg/m2s. The mass M of the slick is related to its size by: M=pAW where p is the density of the oil (given above), A is the surface area of the slick in m2, and W is the thickness of the slick in m. The thickness of a shrinking spill will decrease with time. In this case however, you will be looking at the time period between when it starts to grow and when it reaches a constant size. Assuming a constant slick thickness is probably reasonable for this situation and W= 0.001 m is a realistic thickness to use. What surface area ( in m2) will the slick ultimately have? Assume that the constant release of 0.1 m3/s of oil begins at t=0 and that A=0 at t=0. About how long will it take for the slick to reach a constant size? 2. Relevant equations 3. The attempt at a solution Ok so the first question is pretty straight forward... the set up for the area was as follows: A= (rate of oil to slick from source)/(rate of dissolution + rate of evaporation)... which gives A = 21744.02 m2; which I can then use to find the Mass = 18917.3 kg. The second question is the one that im having problems with... I've set up my differential equation and solved for time, t= 1/0.0046 ln(87) - 1/0.0046 ln (87 -0.0046M) the problem is that when I plug in M this gives ln(0). What am I missing? did I completely screw up the differential equation set up? Any type of ideas or tips would be greatly appreciated.