Answer:
The price of car will be $1,900 after 14.9 years.
Step-by-step explanation:
Formula of depreciate:
[tex]A=P(1-r)^n[/tex]
A= The price of the car after n years.
P= The initial price of the car
r= rate of depreciate
n=time in years.
Given that,
A new car is purchased for $ 15,100.
The value of car depreciates at 13% per year.
Here P=$15,100, A=$1,900, r=13%=0.13, n=?
[tex]A=P(1-r)^n[/tex]
[tex]\Rightarrow 1,900=15,100(1-0.13)^n[/tex]
[tex]\Rightarrow \frac{1,900}{15,100}=(0.87)^n[/tex]
[tex]\Rightarrow (0.87)^n= \frac{1,900}{15,100}[/tex]
[tex]\Rightarrow (0.87)^n= \frac{19}{151}[/tex]
Tanking ln function both sides
[tex]\Rightarrow ln (0.87)^n= ln|\frac{19}{151}|[/tex]
[tex]\Rightarrow nln (0.87)= ln|\frac{19}{151}|[/tex]
[tex]\Rightarrow n= \frac{ln|\frac{19}{151}|}{ln (0.87)}[/tex]
⇒n ≈14.9
The price of car will be $1,900 after 14.9 years.
