SAT Question 3c600337: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. The value of $f\left(0\right)$ is the value of $f\left(x\right)$ when $x=0$. Substituting $0$ for $x$ in the given function yields $f\left(0\right)=270{\left(0.1\right)}^0$, or $f\left(0\right)=270\left(1\right)$, which is equivalent to $f\left(0\right)=270$. Therefore, the value of $f\left(0\right)$ is $270$.