SAT Question e53add44: Nonlinear Functions answer and explanation with Desmos solution

Choice C is correct. A model for a quantity $S$ that increases by a certain percentage per time period $n$ is an exponential function in the form $S(n)=I{\left(1+\frac{r}{100}\right)}^n$, where $I$ is the initial value at time $n=0$ for $r\%$ annual increase. It's given that the annual increase in an employee's salary is $4\%$, so $r=4$. The initial value can be found by substituting $0$ for $n$ in the given function, which yields $S(0)=38,000$. Therefore, $I=38,000$. Substituting these values for $r$ and $I$ into the form of the exponential function $S(n)=I{\left(1+\frac{r}{100}\right)}^n$ yields $S(n)=38,000{\left(1+\frac{4}{100}\right)}^n$, or $S(n)=38,000(1.04{)}^n$. Therefore, the value of $a$ in the given function is $1.04$.