A new car is purchased for 20300 dollars. The value of the car depreciates at 9.5% per year. What will the value of the car be, to the nearest cent, after 11 years?
To calculate the value of the car after 11 years, we can use the formula for exponential decay:
V = P(1 - r)^t
where:
V = value of the car after t years
P = initial value of the car (20300 dollars)
r = annual depreciation rate (9.5% or 0.095)
t = number of years (11)
Plugging in the values:
V = 20300(1 - 0.095)^11
V = 20300(0.905)^11
V = 20300(0.41641602649)
V = 8452.47
Therefore, the value of the car after 11 years will be approximately 8452.47 dollars.