12 In an experiment 500 fruit flies were released into a controlled environment. After 10 days there were 650 fruit flies present. Munirah believes that \(N\), the number of fruit flies present at time \(t\) days after the fruit flies are released, will increase at the rate of \(4.4 \%\) per day. She proposes that the situation is modelled by the formula \(N = A k ^ { t }\).

1. Write down the values of \(A\) and \(k\).
2. Determine whether the model is consistent with the value of \(N\) at \(t = 10\).
3. What does the model suggest about the number of fruit flies in the long run? Subsequently it is found that for large values of \(t\) the number of fruit flies in the controlled environment oscillates about 750 . It is also found that as \(t\) increases the oscillations decrease in magnitude. Munirah proposes a second model in the light of this new information. $$N = 750 - 250 \times \mathrm { e } ^ { - 0.092 t } .$$
4. Identify three ways in which this second model is consistent with the known data.
5. (A) Identify one feature which is not accounted for by the second model.
   (B) Give an example of a mathematical function which needs to be incorporated in the model to account for this feature. \section*{END OF QUESTION PAPER}