Linear Graphs and Its Applications - Linear Graphs in Real Life Problems

Two portable lamps are switched on at the same time. Their remaining battery levels, \(P\%\), after \(t\) hours are modelled by \[\text{Lamp R:}\hspace{0.5em}P=90-6t,\qquad \text{Lamp S:}\hspace{0.5em}P=70-2t,\] for \(0\leq t\leq10\) .

1. Find Lamp \(R\)’s remaining battery level after \(3\) hours.

   [1]

2. Explain the meaning of \(90\) and \(-6\) in Lamp \(R\)’s equation.

   [2]

3. On graph paper, draw both graphs for \(0\leq t\leq10\). Use a horizontal axis from \(0\) to \(10\) hours and a vertical axis from \(0\) to \(100\%\).

   [3]

4. Use your graphs to find when the lamps have the same remaining battery percentage. State this percentage.

   [2]

5. A technician will select the lamp with the higher remaining battery percentage. Which lamp should be selected:

   1. after \(4\) hours?

   2. after \(8\) hours?

   Explain why the choice changes.

   [2]