Since they value of the book is decaying, we are going to adapt the standard exponential decay function to solve this.
Exponential decay function: 
where
 is the final amount remaining after
 is the final amount remaining after  years of decay
 years of decay
 is the initial amount
 is the initial amount
 is the decay rate in decimal form
 is the decay rate in decimal form 
 is the time in years
 is the time in years 
Now, let's adapt the equation to suit our needs
Since the value of the book is decaying with the number of owners and not with time, we are going to let  be the number of previous owners instead of time. So now
 be the number of previous owners instead of time. So now  will represent the final cost of the book after
 will represent the final cost of the book after  owners, and
 owners, and  will be the initial cost of the book.
 will be the initial cost of the book. 
Exponential decay function: 
where
 is the final cost of the book after
 is the final cost of the book after  owners
 owners
 is the initial cost of the book
 is the initial cost of the book
 is the decay rate in decimal form
 is the decay rate in decimal form 
 is the number of previous owners
 is the number of previous owners
Now, we know from our problem that the initial cost of the book is $85, so  . We also know that the resale value of a textbook decreases by 25% with each previous owner; to convert the decay rate (25%) to decimal form, we are going to divide it by 100%:
. We also know that the resale value of a textbook decreases by 25% with each previous owner; to convert the decay rate (25%) to decimal form, we are going to divide it by 100%:


We have everything we need so let's replace the values in our exponential decay equation: 


We can conclude that the correct answer is A) f(x) = 85(1 – 0.25)^x