Immanuel purchased a certain rare coin on January 1. The function $f(x)=65(1.03)^{x}$, where $0\leq x\leq 10$, gives the predicted value, in dollars, of the rare coin $x$ years after Immanuel purchased it. What is the best interpretation of the statement "$f(8)$ is approximately equal to 82" in this context?

Question

Immanuel purchased a certain rare coin on January 1. The function $f(x)=65(1.03)^{x}$, where $0\leq x\leq 10$, gives the predicted value, in dollars, of the rare coin $x$ years after Immanuel purchased it. What is the best interpretation of the statement "$f(8)$ is approximately equal to 82" in this context?

Accepted Answer

8 years after Immanuel purchased the rare coin, its predicted value is approximately 82 dollars.

Answer

When the rare coin's predicted value is approximately 82 dollars, it is 8% greater than the predicted value, in dollars, on January 1 of the previous year.

Answer

When the rare coin's predicted value is approximately 82 dollars, it is 8 times the predicted value, in dollars, on January 1 of the previous year.

Answer

From the day Immanuel purchased the rare coin to 8 years after Immanuel purchased the coin, its predicted value, increased by a total of approximately 82 dollars.