To calculate the cost in Rands of consuming between 0-50 kWh of electricity, we can define a piecewise linear function. This function will take into account the cost per kWh within the specified range.
Let's consider:
- [tex]\( kWh\_consumed \)[/tex] as the number of kilowatt-hours consumed.
- Given the cost per kWh is R0.96 for the first 0-50 kWh range.
We can define the cost function [tex]\( C(kWh\_consumed) \)[/tex] as follows:
[tex]\[
C(kWh\_consumed) =
\begin{cases}
0.96 \times kWh\_consumed & \text{if } 0 \leq kWh\_consumed \leq 50
\end{cases}
\][/tex]
This piecewise equation states that if the number of kilowatt-hours consumed is between 0 and 50, the total cost is calculated by multiplying the consumed kilowatt-hours ([tex]\( kWh\_consumed \)[/tex]) by 0.96 (Rands).
Thus, the equation to calculate the cost in Rands for consuming between 0-50 kWh of units is:
[tex]\[
C(kWh\_consumed) = 0.96 \times kWh\_consumed \quad \text{for } 0 \leq kWh\_consumed \leq 50
\][/tex]
