SAT Question 5acbdc30: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. For a function of the form $f\left(x\right)=a(b{)}^x$, where $a$ and $b$ are constants and $b<1$, the value of $f(x)$ decreases by $100(1-b)\%$ for every increase of $x$ by $1$. In the given function, $a=56$ and $b=0.19$. Therefore, for the given function, the value of $f(x)$ decreases by $100(1-0.19)\%$, or $81\%$, for every increase of $x$ by $1$. It’s given that the value of $f(n)$ is $p\%$ less than the value of $f(n-1)$. The increase from $x=n-1$ to $x=n$ can be expressed as $n-(n-1)$, which is equivalent to $n-n+1$, or $1$. Since there is an increase by $1$ from $n-1$ to $n$, it follows that the value of $f(n)$ is $81\%$ less than the value of $f(n-1)$. Thus, the value of $p$ is $81$.