assume a pair of roaches spawns another pair at the rate of 1pair/week, assume that roaches have no predators and their lifetime is longer than 2 years. Assume that the top 2 meters of Earth's land surface is covered with dirt, loaded with bacteria, plant detritus and potential food that satisfies roaches.
1) Starting at t=0 with 1 pair of roaches, how long will it take until the mass of the total roach population exceeds the mass of the top 2 meters of Earth's land surface? (let the mass of a roach equal 1 gram, density of Earth's top surface equal 2
, the amount of land surface equal about 25% and the radius of Earth equals 6,378km).
2) at what generation the roaches realize that they have a problem?