SAT Question f1c81b3b: Nonlinear Functions answer and explanation with Desmos solution

It's given that the exponential function $g$ is defined by $g\left(x\right)=19\cdot a^x$, where $a$ is a positive constant, and $g\left(3\right)=2,375$. It follows that when $x=3$, $g\left(x\right)=2,375$. Substituting $3$ for $x$ and $2,375$ for $g\left(x\right)$ in the given equation yields $2,375=19\cdot a^3$. Dividing each side of this equation by $19$ yields $125=a^3$. Taking the cube root of both sides of this equation gives $a=5$. Substituting $4$ for $x$ and $5$ for $a$ in the equation $g\left(x\right)=19\cdot a^x$ yields $g\left(4\right)=19\cdot 5^4$, or $g\left(4\right)=11,875$. Therefore, the value of $g\left(4\right)$ is $11,875$.