2023 ACSBR EM S1 EOY Q14
2023 ACSBR EM S1 EOY Q14
7 marks
A company charges \(\$ y\) for \(x\) units of electricity used.
The charge \(\$ y\) can be represented by the function \(y = ux + 20\), where \(u\) is a constant. Some corresponding values of \(x\) and \(y\) are given in the table below.
| \(x\) | \(0\) | \(100\) | \(200\) | \(300\) | \(400\) |
|---|---|---|---|---|---|
| \(y\) | \(20\) | \(50\) | \(80\) | \(110\) | \(140\) |
- On the grid, draw the graph of \(y = ux + 20\) for \(0 \le x \le 400\).[2]
- Find the total cost if a household uses \(140\) units of electricity.[1]
- What does the constant term, \(20\), represent?[1]
- Find the value of \(u\).[2]
- What does the gradient of the graph represent in this context?[1]
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Answer:(a) \(y=0.3x+20\) for \(0\le x\le400\); (b) \(62\) dollars; (c) a fixed charge of \(20\) dollars; (d) \(u=0.3\); (e) the cost increases by \(0.30\) dollars per unit of electricity.
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