SAT Question 71b74a44: Nonlinear Functions answer and explanation with Desmos solution

Choice C is correct. It’s given that $y=7,400(0.87{)}^x$ estimates the value, in dollars, of a certain piece of equipment $x$ years after it was purchased. The estimated value of the piece of equipment at the time it was purchased corresponds to the value of $y$ when $x=0$. Substituting $0$ for $x$ in the equation $y=7,400(0.87{)}^x$ yields $y=7,400(0.87{)}^0$, which is equivalent to $y=7,400(1)$, or $y=7,400$. Therefore, the estimated value, in dollars, of the piece of equipment at the time it was purchased was $7,400$.