5.
\begin{figure}[h]
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\caption{Figure 2}
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The share value of two companies, company \(A\) and company \(B\), has been monitored over a 15-year period.
The share value \(P _ { A }\) of company \(\boldsymbol { A }\), in millions of pounds, is modelled by the equation
$$P _ { A } = 53 - 0.4 ( t - 8 ) ^ { 2 } \quad t \geqslant 0$$
where \(t\) is the number of years after monitoring began.
The share value \(P _ { B }\) of company \(B\), in millions of pounds, is modelled by the equation
$$P _ { B } = - 1.6 t + 44.2 \quad t \geqslant 0$$
where \(t\) is the number of years after monitoring began.
Figure 2 shows a graph of both models.
Use the equations of one or both models to answer parts (a) to (d).
- Find the difference between the share value of company \(\boldsymbol { A }\) and the share value of company \(\boldsymbol { B }\) at the point monitoring began.
- State the maximum share value of company \(\boldsymbol { A }\) during the 15-year period.
- Find, using algebra and showing your working, the times during this 15-year period when the share value of company \(\boldsymbol { A }\) was greater than the share value of company \(\boldsymbol { B }\).
- Explain why the model for company \(\boldsymbol { A }\) should not be used to predict its share value when \(t = 20\)
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