1. The problem statement, all variables and given/known data The flow of water into a barrel = 36.8 lb/sec. The height of the water = h = weight of the water in the barrel/(density of water)(bottom area of barrel) There is a "leak" at the bottom of the barrel at h = 0. Flow out of the barrel is related to the depth of the water in the barrel. The deeper the water in the barrel the faster it will flow out. For this barrel the water flow out in lb/sec is = 9.2*h. The area of the barrel is A = 4.60 ft^2. The density of water is p = 62.4 lb/ft^3. Develop a mathematical model to represent the height of the water in the barrel as a function of time. 2. Relevant equations I'm given an equation for the theoretical height of the water: htheo(t) = 4(1-exp(-.032t)) 3. The attempt at a solution I'm drawing a blank on this, unfortunately. I have to develop a model for h(t) to use in a Matlab script to produce a matrix for height values from t = 0 to 250 seconds. My original thought was to set h = (36.8t - 9.2h)/(density*area) and then solve for h. But of course that resulted in a linear equation with no maximum height of the water. This is obviously incorrect since the water will eventually even out as the leak factor is equal to the incoming water, when h = 4 ft. I simply cannot wrap my mind around how to set up an equation for this. Any help at all would be greatly appreciated!