The value of car after 12 years is $ 2982.92
Solution:
Given that,
A new car is purchased for 17000 dollars
The value of the car depreciates at 13.5% per year
To find: Value of car after 12 years
The decreasing function is given as:
[tex]y = a(1-r)^t[/tex]
Where,
y is the future value
a is the initial value
r is the decreasing rate in decimal
t is the number of years
From given,
[tex]a = 17000\\\\t = 12\\\\r = 13.5 \% = \frac{13.5}{100} = 0.135[/tex]
Substituting the values we get,
[tex]y = 17000(1-0.135)^{12}\\\\y = 17000(0.865)^{12}\\\\y = 17000 \times 0.1754661\\\\y = 2982.9241 \approx 2982.92[/tex]
Thus value of car after 12 years is $ 2982.92
