Gce Model Questions Vol1 2022 Civic Education Question 30

The number of reported cult‑related incidents in a city each year can be modelled by \( I(t)=I_{0}e^{-kt}+C \), where \(t\) is the number of years since the start of an anti‑cult programme, \(C\) is the irreducible baseline number of incidents, \(I_{0}\) is the excess incidents above the baseline at \(t=0\), and \(k\) is a positive decay constant. At the start (\(t=0\)) there were 120 incidents, and the baseline \(C\) is known to be 20 incidents per year. Two years later (\(t=2\)) the recorded incidents fell to 70. Determine the decay constant \(k\) (rounded to three decimal places) and use it to predict the number of incidents expected in year 5, rounded to one decimal place. Present your answer as "\(k = ...\), incidents = ...".