### Process Controls

Y max = 250

dt

J

N

Q

K

K3

K4

K7

K8

TC

TC = Critical Time
The time when humanity develops the knowledge to use fosil fuel. If TC is above 320 it means fossil fuels are not used.

# Two sources mini-model simulation

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Dt

K7

K8

### Description

A system of this type uses two energy sources, one renewable, the other nonrenewable. When the nonrenewable source is used up, the growth declines back to a steady state based on the renewable source.

### Variables

• N = nonrenewable energy source
• J = steady inflow of energy
• Q = stored biomass
• K*JR*Q = part of J that goes into the system
• K3 = increasing factor of Q
• K7 = increasing factor of Q
• K8 = decreasing factor of Q

### Equations

• DN = -K4*N*Q
• JR = J/(1 + K*Q)
• DQ = K7*N*Q + K3*JR*Q - K8*Q

### Simunlation

The graph shows the changes of N (red) and Q (green) over a time period.

### Examples

• A population of microbes which decompose a pile of leaves and the leaves falling from the trees.
• The world economy growing up on both fossil fuels and renewable sources.

### "What if" Experiments

• Think about the renewable and nonrenewable sources of our economy:
• If we find more fuels (N), will our industrial society peak higher or last longer?
• If pollution increases giving us less available clear sun and rain (J), how will this affect the growth and future of the economy?