## Help with a Differential Equations project modeling Air, Food, Water consumption...

Help with a Differential Equations project modeling Air, Food, Water consumption, and a Hydroponic system

I am working on a differential equations project, and I need to model the food, oxygen(air), and a hydroponic system for astronauts on Mars. This is what I came up with so far.

Mf- Food, Mo-Oxygen, Mh-hydroponic plants (for food and oxygen)

ΔMf = -k Δt

ΔMh = kMh Δt - a Δt

ΔMh/ Δt = kMh-a

Δt => 0

dMh/dt = kMh -a

ΔMf = -k Δt + a Δt

ΔMf/ Δt= a - k

Δt=> 0

dMf/dt = a - k

ΔMo = -k1 Δt -k2 Mh Δt

ΔMo/ Δt = -k1 - k2 Mh

Those will yield a system of equations...

dMf/dt = a-k

dMh/dt = kMh - a

dMo/dt = -k1 - k2Mh

I think I need to take this system of equations a bit further and I also want to consider water in this somehow.

Water = K(initial value) + F1( water from the fuel cells) - F2 (what the humans consume) + F3 ( the human's waste that can be recycled) - Hy( what the hydroponics consume)

I need to turn that into a differential equation.

Am I on the right track? Any suggestions?