After $n$ years, the population, $P$, in thousands, of a certain species of foxes can be modelle

Question

After $n$ years, the population, $P$, in thousands, of a certain species of foxes can be modelled by an equation $P = A\mathrm{e}^{kn}$, where $A$ and $k$ are constants. The table below shows the values of $n$ and $P$. $n$ $5$ $10$ $15$ $20$ $25$ $P$ $6.23$ $4.85$ $3.78$ $2.94$ $2.29$ On the grid on the next page, plot $\ln P$ against $n$ and draw a straight line graph.[2] Use your graph to estimate the initial population of the foxes and the value of $k$.[4] If this model for the population remains valid, after how many whole years would the population of the foxes first decreased to $1000$?

Accepted Answer

(a) $\ln P\approx2.08-0.050n$. (b) Initial population approximately $8000$ foxes; $k\approx-0.050$. (c) $42$ whole years.

2024 CGSS P1 Q11

2024 CGSS P1 Q11

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