Nonlinear functions SAT question

Choice D is correct. It’s given that the function $f(x)=65{(1.03)}^x$ gives the predicted value, in dollars, of a certain rare coin $x$ years after Immanuel purchased it. It follows that $f(x)$ represents the predicted value, in dollars, of the coin $x$ years after Immanuel purchased it. Since the value of $f(8)$ is the value of $f(x)$ when $x=8$, it follows that “$f(8)$ is approximately equal to $82$” means that $f(x)$ is approximately equal to $82$ when $x=8$. Therefore, the best interpretation of the statement “$f(8)$ is approximately equal to $82$” in this context is $8$ years after Immanuel purchased the rare coin, its predicted value is approximately $82$ dollars.

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.