the resale value of a textbook decreases by 25% with each previous owner. a new textbook is sold for $85…

the resale value of a textbook decreases by 25% with each previous owner. a new textbook is sold for $85. which function represents the resale value of the textbook after x owners?\n○ f(x)=85(1 - 0.25)^x\n○ f(x)=85(1 + 0.25)^x\n○ f(x)=85(0.25)^x\n○ f(x)=(85 - 0.25)^x
Answer
Explanation:
Step1: Identify the decay - formula
The general formula for exponential decay is $f(x)=a(1 - r)^x$, where $a$ is the initial amount, $r$ is the rate of decay, and $x$ is the number of time - periods.
Step2: Determine the values of $a$ and $r$
The initial value of the textbook $a = 85$ (the price when it's new). The rate of decay $r=0.25$ (since it decreases by 25% or 0.25).
Step3: Substitute the values into the formula
Substituting $a = 85$ and $r = 0.25$ into the formula $f(x)=a(1 - r)^x$, we get $f(x)=85(1 - 0.25)^x$.
Answer:
$f(x)=85(1 - 0.25)^x$ (First option)