The table shows the population, $P$, in thousands, of a small town decreases with time, $t$ year

Question

The table shows the population, $P$, in thousands, of a small town decreases with time, $t$ years. $t$ $6$ $9$ $12$ $15$ $18$ $25$ $33$ $P$ $274$ $203$ $151$ $112$ $83$ $41$ $18$ Show your working clearly and draw a straight line graph of $\ln P$ against $t$ on the grid provided.[3] Find the gradient of your straight line and hence express $P$ in the form of $A\mathrm{e}^{-kt}$, where $A$ and $k$ are constants, giving your answers correct to the nearest hundred and to $1$ decimal place respectively.[4] If this model for the population remains valid, find the number of years it will take for the population of the small town to drop below $100 \ 000$. Give your answer correct to the nearest year.[2]

Accepted Answer

(a) Straight-line plot shown. (b) Gradient $\approx-0.0989$; $P=500e^{-0.1t}$. (c) $16$ years (nearest year).

2024 FMSS PRELIMS P2 Q8

2024 FMSS PRELIMS P2 Q8

Solution:

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