Question 67·Medium·Advanced Math

$f(2)$ means the output when $x=2$. The problem gives that output as $72$, so replace $x$ with $2$ in the rule:

The base $b$ is the factor used each time $x$ increases by $1$. Type $8b^2\sim72\{b>0\}$ in Desmos. The $\sim$ asks Desmos to fit $b$, and the restriction keeps the positive value the problem requires. Under PARAMETERS, Desmos shows $b=3$.

Replace $b$ with $3$ by typing $f(x)=8(3)^x$ on the next line. Keep the exponent $x$: it counts how many times the factor $3$ is applied to the starting value $8$.

Type $f(5)$; Desmos prints $1{,}944$. From input $2$ to input $5$ is three one-unit steps, so the output $72$ is multiplied by $3$ three times. The value of $f(5)$ is $1{,}944$. Choice C.