SAT Question 53c07bf9: Nonlinear Functions answer and explanation with Desmos solution

Choice C is correct. It’s given that the value of a certain fishing boat was $$24,000$ when it was purchased. It's also given that each year, the value of the fishing boat decreased by $20\%$ of the previous year's value. It follows that this situation can be represented by the equation $v=a{\left(1-\frac{r}{100}\right)}^y$, where $v$ is the value of the boat, in dollars, $y$ years since it was purchased, $a$ is the value of the boat, in dollars, when it was purchased, and $r$ is the percent by which the value of the boat decreases each year from the previous year's value. Substituting $24,000$ for $a$ and $20$ for $r$ in this equation yields $v=24,000{\left(1-\frac{20}{100}\right)}^y$, or $v=24,000{\left(0.8\right)}^y$. Therefore, $v=24,000{\left(0.8\right)}^y$ represents this situation.