In $2020$, there were an estimated $7$ million insects of a particular species in a certain coun

Question

In $2020$, there were an estimated $7$ million insects of a particular species in a certain country. In $2021$, the numbers were estimated to have fallen to $5$ million. Scientists believe that the number of these insects, $N$ million, can be modelled by the formula $N = 3 + a\mathrm{e}^{-kt}$, where $t$ is the time in years after $2020$. Find the exact values of $a$ and of $k$.[4] What is the approximate size of the population for large values of $t$?[1]

Accepted Answer

(a) $a=4$, $k=\ln2$ (b) $3$ million insects

(A Math) 2025 CCHY PRELIMS P2 Q1

(A Math) 2025 CCHY PRELIMS P2 Q1

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