For a television network, 5 × 10⁵ channels are granted. If the central frequency of the microwave link is 25 GHz and the allotted bandwidth for each channel is 2 kHz, then how much percentage of the link is used for the network?

(a) Let  $x\%$ of link is used for network. Given central frequency = 25 GHz
 =  $25\times {10}^{9}Hz$
Bandwidth of channels = x% of 25 GHz
 = $\frac{x}{100}\times 25\times {10}^9=25x\times {10}^7$
Number of channel 
= $\frac{\text{Total\hspace{0.17em}\hspace{0.17em}Bandwidth}}{\text{Bandwidth\hspace{0.17em}needed\hspace{0.17em}per\hspace{0.17em}channel}}$
$\text{5}\times {\text{10}}^5=\frac{25x\times {10}^7}{2\times {10}^3}$           
$=10\times {\text{10}}^8=25x\times {10}^7=25x100\Rightarrow 4\%$