Answer:
Cost of the car in year 2016 will be $2811.
Step-by-step explanation:
Cost price of the car = $22800
Value of the car has been depreciating exponentially, so the formula for value of the car after t years,
[tex]P(t)=A(1-\frac{r}{100})^{t}[/tex]
Here P(t) = Final value after t years
A = Cost price or initial value
r = rate of depreciation
t = duration in years
[tex]P(6)=22800(1-\frac{r}{100})^{6}[/tex]
[tex]10400=22800(1-\frac{r}{100})^{6}[/tex]
[tex]\frac{10400}{22800}=(1-\frac{r}{100})^{6}[/tex]
0.87737 = [tex](1-\frac{r}{100})[/tex]
r = 100(1 - 0.87737)
r = 12.26%
Now cost of the car in year 2016 (After 16 years)
P(16) = [tex]22800(1-\frac{12.26}{100})^{16}[/tex]
= [tex]22800(0.87737)^{16}[/tex]
= 2810.99
= $2811
Therefore, cost of the car in year 2016 will be $2811.
