Insect abundance and distribution are regulated by several biotic and abiotic factors and their interactions. Among the many abiotic factors, temperature and humidity stand out as the most important ones constraining abundance and distribution of insect. Often, these two factors regulate the ecology of insect communities. Knowledge of the impacts of these factors can be essential and serve as useful tools for understanding seasonal population dynamics and in making pest management decisions. In one of the studies on two newly discovered leaf beetle species, codenamed G12 and G13, the population dynamics of these species due to the impact of temperature and relative humidity can be modelled by the following nonlinear equations: Paz (0.7) = 22-18cos (p+1) Paz (P.T)=175-27+pT where Peiz refers to the population of species G12. Para refers to the population of species G13. p is the relative humidity and I is relative temperature; all parameters used are unitless for simplification a) b) c) Based on the simplified model above, formulate the system of equations in order to determine the estimated values of p. the relative humidity and T. relative temperature such that the population of both species G12 and G13 will reach 500 and 325, respectively. [6 Marks] Based on the system of equations in part (a), determine the Jacobian terms needed for solving using the Newton Raphson method. Perform FIVE (3) iterations of Newton Raphson using initial guesses of po = 1.5 and 7 = 15. [10 Marks] Based on your solution in Part (b), what can you comment about the convergence of the solution? Are the solutions making sense?