1. The problem statement, all variables and given/known data "Suppose that a liquid has an appreciable compressibility. Its density therefore varies with depth and pressure. The density at the surface is ρ0 (a) Show that the density varies with pressure according to ρ=ρ0ekp where P is gauge pressure at any depth and k is the compressibility, a constant. (b) Find P as a function of depth y. 2. Relevant equations ρ = m/V (Density definition) k = (1/V)(ΔV/ΔP) (Compressiblity definition) dP/dy = ρg (Pascal's Law) My professor also hinted that I should replace any deltas with differentials, that I need to eliminate V, and to find dρ/dV (which is -m/V2 3. The attempt at a solution From the second equation, I multiplied both sides by dP (after changing ΔV to dV and ΔP to dP) to obtain the following: k dP = (1/V) dV I then integrated both sides: ∫k dP (from P0 to P) = ∫(1/V) dV (from 0 to V) kP(gauge)=ln(V) ekP(gauge) = V I get the feeling that I'm going in the correct direction, but haven't found a viable solution from this point. I fooled around with the density definition and Pascal's Law to no avail. Any assistance would be much appreciated.