A carrier signal \( c(t) = 25 \sin(2.512 \times 10^{10} t) \) is amplitude modulated by a massage signal \( m(t) = 5 \sin(1.57 \times 10^{8} t) \) and transmitted through an antenna. What will be the bandwidth of the modulated signal?
\( 8 \, \text{GHz} \)
\( 1987.5 \, \text{MHz} \)
\( 2.01 \, \text{GHz} \)
\( 50 \, \text{MHz} \)
