Question 322·Hard·Math

Both formulas define the same $g$, so they must agree at $x=1$. That choice makes the exponent on the right equal to $1$, exposing its factor, the amount kept after one step in $x$: $g(1)=(0.77)^5=1-\frac{q}{100}$. Keep the $5$: when $x=1$, the exponent $5x$ is $5$, not $1$.

Type the given function as $g(x)=(0.77)^{5x}$ in Desmos, then type $g(1)$. Desmos shows $g(1)=0.2706784157$. So about $27\%$ remains after one step in $x$; that isn't the percent lost.

The form $1-\frac{q}{100}$ says $q$ is the percent lost, not the percent remaining. Subtract the factor from $1$ to find the fraction lost. So $q=100(1-g(1))$. Type $100(1-g(1))$ on the next Desmos line; it shows $72.93215843$, which is closest to $73$. Choice C.