Moderate -0.5 This question requires students to linearize an exponential model by taking logarithms, then use two points from a graph to find constants a and b. While it involves multiple steps (reading graph, applying log properties, solving simultaneous equations), these are standard A-level techniques with no novel problem-solving required. The question is slightly easier than average because it's a well-practiced application of logarithms to exponential models, though reading values from a graph and maintaining accuracy to 4 significant figures adds minor complexity.
\includegraphics{figure_1}
Red squirrels were introduced into a large wood in Northumberland on 1st June 1996.
Scientists counted the number of red squirrels in the wood, \(P\), on 1st June each year for \(t\) years after 1996.
The scientists found that over time the number of red squirrels can be modelled by the formula
$$P = ab^t$$
where \(a\) and \(b\) are constants.
The line \(l\), shown in Figure 1, illustrates the linear relationship between \(\log_{10} P\) and \(t\) over a period of 20 years.
Using the information given on the graph and using the model,
find a complete equation for the model giving the value of \(b\) to 4 significant figures. [4]
\includegraphics{figure_1}
Red squirrels were introduced into a large wood in Northumberland on 1st June 1996.
Scientists counted the number of red squirrels in the wood, $P$, on 1st June each year for $t$ years after 1996.
The scientists found that over time the number of red squirrels can be modelled by the formula
$$P = ab^t$$
where $a$ and $b$ are constants.
The line $l$, shown in Figure 1, illustrates the linear relationship between $\log_{10} P$ and $t$ over a period of 20 years.
Using the information given on the graph and using the model,
find a complete equation for the model giving the value of $b$ to 4 significant figures. [4]
\hfill \mbox{\textit{SPS SPS SM 2020 Q9 [4]}}