Neco Model Questions Vol1 2017 Agricultural Science Question 7

During a six‑week maize season a farmer monitors the stem‑borer population. The population at the start of each week (larvae per plant) is: Week 1 = 3, Week 2 = 4.5, Week 3 = 6.75. If uncontrolled, the population multiplies by a factor of 1.5 each week. The economic threshold is 5 larvae per plant. The farmer can use (i) cultural control, which reduces the weekly multiplication factor to 1.0, (ii) biological control, which reduces the population by 30 % each week, or (iii) chemical control, which reduces the population instantly by 70 % and thereafter the population remains at that reduced level (no further growth). Assuming the season lasts six weeks, determine the earliest week in which chemical control must be applied so that the population stays below the threshold for the remainder of the season. Also, compare this with using biological control starting at the beginning of week 3 and calculate how many weeks of sub‑threshold population are saved by the chemical treatment.