The antenna current of an AM transmitter is 8 A when only carrier is sent but increases to 8.96 A when the carrier is sinusoidally modulated. The percentage modulation is

71%

We know that $(\frac{I_t}{I_c})^2=1+\frac{m^2}{2}$

Here, $I_t= 8.96A$ and $I_c =8A$

$∴(\frac{8.96}{8})^2=1+\frac{m^2}{2}$ or $1.254+1+\frac{m^2}{2}$

or $\frac{m^2}{2}=0.254$ 

or $m^2=0.508$

or $m=0.71=71\%$