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NSW Y12 Maths Standard 1 NSW Y12 Maths Standard 2 NSW Y12 Maths Advanced NSW Y12 Maths Extension 1 NSW Y12 Maths Extension 2

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Rates and Ratios Networks Investments and Loans Non-Right Angled Trigonometry Simultaneous Equations Bivariant Data Analysis Annuities Non-Linear Relationships Normal Distribution Critical Path Analysis

NSW Y12 Maths - Standard 2 Rates and Ratios Energy Rate

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Energy Rate Theory

Heat energy such as that produced by burning natural gas is measured in megajoules. (l million joules \(\rightarrow\) MJ)\\ Electrical energy is measured in watts. Consumption is a rate expressed as an amount over time.\\ A kilowatt hour (kwh) represents the amount of energy when a \(1000 \mathrm{~W}\) power load is used for one hour.\\ \begin{multicols}{2} \textbf{Example 1}\\ An energy company charges for gas over a 3 month period at \(\$ 0.035\) per. MJ. Anna received a bill for \(\$ 105\). Determine the amount of gas that was used.\\ \textbf{Example 1 solution}\\ $\begin{aligned} \text { Let } A=\text { amount } \qquad 105 & =A \times 0.035 \\ A & =105 \div 0.035 \\ & =3000 \mathrm{~MJ} \end{aligned}$\\ \columnbreak \textbf{Example 2}\\ Fred uses a \(12 W\) fan for a total of 8 hours a day. He is charged at a rate of \(15.6\) cents per kilowatt-hour. What is the cost of running the fan for a week? \\ \textbf{Example 2 solution}\\ $\begin{aligned} \text{cost}& =\frac{12}{1000} \times 8 \times 7 \times 0.156 \\ & =\$ 0.10 \end{aligned}$\\ \end{multicols}

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