Question

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?
$f(x) = 85(1 - 0.25)^x$
$f(x) = 85(1 + 0.25)^x$
$f(x) = 85(0.25)^x$
$f(x) = (85 - 0.25)^x$

Explanation:

Step1: Identify decay formula

The general exponential decay function is $f(x) = P(1 - r)^x$, where $P$ is initial value, $r$ is decay rate.

Step2: Plug in given values

Here, $P = 85$, $r = 0.25$. Substitute into formula:
$f(x) = 85(1 - 0.25)^x$

Step3: Eliminate incorrect options

• $f(x)=85(1 + 0.25)^x$ is growth, not decay.
• $f(x)=85(0.25)^x$ would mean 75% loss per owner, not 25%.
• $f(x)=(85 - 0.25)^x$ misapplies the decay rate.

Answer:

$f(x) = 85(1 - 0.25)^x$