Gce Model Questions Vol1 2025 Agricultural Science Question 10

An agricultural extension programme aims to promote a new high‑yielding maize variety to a maximum of \(200\) smallholder farms over three years. Adoption follows the logistic model \(A(t)=\frac{K}{1+e^{-r(t-t_0)}}\) where \(K=200\) is the ceiling, \(r\) the intrinsic adoption rate and \(t_0\) the inflection year (50 % adoption). Pilot data show \(30\) farms adopted after year 1 and \(80\) farms after year 2. (i) Determine the values of \(r\) and \(t_0\). (ii) Predict the number of adopters at the end of year 3. (iii) Each adopting farm yields an extra \(1.5\) tonnes of maize valued at ₦150 000 per tonne. Calculate the total additional economic benefit at year 3 and state whether it meets a target benefit of ₦30 000 000.