Homework 3.

1. You are analyzing the population dynamics of the white geese that live by the Charles River. The city wants to keep the population stable, at the point where the growth of the population reaches Maximum Sustainable Yield (MSY), which is where the growth hits maximum. The size of the initial population is 10 birds and the ecosystem around the river only can support 500 birds.  The net birth rate is 0.006 birds/birds/timeperiod and the population grows according to a logistic growth curve.

1. What is the maximum growth rate (the MSY)?
2. What is the corresponding total size of the population when you hit the MSY?
3. Assume that the total initial geese population is equal to the carrying capacity.  Given the MSY you estimated earlier, initiate a hunting program where you allow exactly the MSY to be caught each year.  Graph the dynamics of the total population stock until it reaches a new equilibrium. How large is the new equilibrium size, explain the dynamics you observe.

2. Winter is almost here and you would like to begin using your radiator. However you want to get some idea of how many times during the day your furnace will start up – and thus you create a STELLA model of the heat circulation in your apartment. The thermostat in your house is set to 65 degrees, and thus if the temperature in your house declines below 65 degrees the furnace will be activated heating your house to 70 degrees in 1 minute.  The temperature in your house changes as a function of the difference between the temperature outside and the temperature in your house, and a factor of proportionality that is equal to 0.01.

The initial temperature in your house is 70 degrees and the outside temperature is 50 degrees, and it stays at 50 degrees.

a)     Begin the simulation at 7AM in the morning and estimate how many times during the next 12 hours the furnace is activated.

Due Tuesday 10/7