7. Figure 1 Solar panels are installed on the roof of a building. The power, \(P\), produced on a particular day, in kW , can be modelled by the equation $$P = 0.95 + 2 ^ { t - 12 } + 2 ^ { 12 - t } - ( t - 12 ) ^ { 2 } \quad 8.5 \leqslant t \leqslant 15.2$$ where \(t\) is the time in hours after midnight. The graph of \(P\) against \(t\) is shown in Figure 1. A table of values of \(t\) and \(P\) is shown below, with the values of \(P\) given to 4 significant figures where appropriate.

1. Use the given equation to complete the table, giving the values of \(P\) to 4 significant figures where appropriate. The amount of energy, in kWh , produced between 10:00 and 12:00 can be found by calculating the area of region \(R\), shown shaded in Figure 1.
2. Use the trapezium rule, with all the values of \(P\) in the completed table, to find an estimate for the amount of energy produced between 10:00 and 12:00. Give your answer to 2 decimal places.
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