DEs to model food, oxygen, and hydroponic plants

[bulldogs]

Hello, I am completing a project for class. In this project, we need to use differential equations to model different subjects for a trip to mars. I was assigned Food, Oxygen, and plant growth. However, I need some help with the equations. I have a system of equations at the bottom, but where do I go from here? Thanks for any help!


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

 

[jvicens]

Dear student,

Great job on setting up your system of equations! Now, we can use these equations to model the change in food, oxygen, and plant growth over time. Here are a few steps you can follow to continue with your project:

1. Determine the initial values: Before we can solve the equations, we need to know the initial values of Mf, Mh, and Mo. These represent the amount of food, hydroponic plants, and oxygen at the beginning of the trip to Mars. Let's say the initial values are Mf(0) = 100, Mh(0) = 50, and Mo(0) = 200.

2. Solve the equations: Now, we can use the initial values and solve the equations to find the values of Mf, Mh, and Mo at any given time t. This will give us a better understanding of how these quantities change over time during the trip to Mars.

3. Interpret the results: Once you have solved the equations, you can interpret the results to see how the food, oxygen, and plant growth change over time. For example, if the value of Mf decreases over time, it means that the food supply is decreasing and you may need to find a way to increase it to sustain the trip to Mars.

4. Adjust the parameters: In your equations, k, a, k1, and k2 represent parameters that can affect the rate of change of Mf, Mh, and Mo. You can adjust these parameters to see how they affect the results. For example, increasing the value of k1 would mean that oxygen is being used up at a faster rate, so you may need to find a way to increase the oxygen supply on the trip.

5. Consider other factors: Your equations only take into account the change in food, oxygen, and plant growth over time. However, there may be other factors that can affect these quantities, such as temperature, humidity, and other environmental factors. You can try to incorporate these factors into your equations to make your model more accurate.

I hope this helps you with your project. Good luck!