2 Two separate rabbit populations are observed for 80 weeks

Last updated: 8/19/2023

2 Two separate rabbit populations are observed for 80 weeks starting at the same time and with the same initial populations The growth rates of two rabbit populations are modeled as follows where t 0 corresponds to the beginning of the observation period ri t 4 sin t 0 11 1 where r is rabbits per week and is time in weeks r2 t t 2 where r is rabbits per week and is time in weeks Below is a graph of the curves representing the rates of growth of the two populations over the observation period 10 20 30 50 60 70 80 A Using your calculator find approximately the first positive time for which the rates of growth for the two populations are the same B What s the physical significance of the area between the two curves from time t 0 until the first time where the two rates are the same What does the area represent I C Suppose you want to find the first time call it 7 after the beginning of the observation period at which the two rabbit populations have identical populations Write an equation to solve for the unknown variable T