SAT Question 08d03fe4: Nonlinear Functions answer and explanation with Desmos solution

Choice C is correct. For the form of the function in choice C, $f\left(x\right)=128{\left(1.6\right)}^{x-1}$, the value of $f\left(1\right)$ can be found as $128{\left(1.6\right)}^{1-1}$, which is equivalent to $128{\left(1.6\right)}^0$, or $128$. Therefore, $k=128$, which is shown in $f\left(x\right)=128{\left(1.6\right)}^{x-1}$ as the coefficient.