Neco 2017 Agricultural Science Question 27

An insect pest population in a field follows the discrete logistic model \(P_{t+1}=P_{t}+rP_{t}\bigl(1-\frac{P_{t}}{K}\bigr)\) with initial population \(P_{0}=200\), intrinsic rate \(r=0.3\) per week and carrying capacity \(K=2000\). The economic injury level (EIL) is 800 pests per hectare. A pesticide reduces the current population by 75\% and costs ₦150 per hectare. The crop yields a profit of ₦5000 per hectare if the pest population stays below the EIL for the whole 12‑week season; otherwise the farmer incurs a loss of ₦2000. The farmer can either (i) apply the pesticide at the start of the season, or (ii) wait and apply it only if the population exceeds the EIL at the end of week\,4. Determine the net profit for each strategy and state which strategy is economically better.