Answer:
b. $7732
Step-by-step explanation:
Value of a depreciating product:
The value of a depreciating product, after t years, is given by:
[tex]V(t) = V(0)(1 - r)^t[/tex]
In which V(0) is the initial value and r is the decay rate, as a decimal.
Joe bought a car for $9,000 in 2013. His purchase has depreciated 2.5% every year since then.
This means that [tex]V(0) = 9000, r = 0.025[/tex]. So
[tex]V(t) = V(0)(1 - r)^t[/tex]
[tex]V(t) = 9000(1 - 0.025)^t[/tex]
[tex]V(t) = 9000(0.975)^t[/tex]
What was his car worth in 2019 to the nearest dollar?
2019 is 2019 - 2013 = 6 years after 2013, so this is V(6).
[tex]V(6) = 9000(0.975)^6 = 7732[/tex]
The correct answer is given by option b.
