Answer:
4 years will it take for the car to be worth half of its original value.
Step-by-step explanation:
Given : Will purchased a car for $21,000. If [tex]V = 21,000(0.85)^x[/tex] gives the value of the car after x years.
To find : How many years will it take for the car to be worth half of its original value?
Solution :
[tex]V = 21,000(0.85)^x[/tex] gives the value of the car after x years.
The car to be worth half of its original value i.e. [tex]V=\frac{21000}{2}=10500[/tex]
[tex]10500 = 21000(0.85)^x[/tex]
[tex]\frac{10500}{21000}=(0.85)^x[/tex]
[tex]0.5=(0.85)^x[/tex]
Taking log both side,
[tex]\log (0.5)=x\log(0.85)[/tex]
[tex]x=\frac{\log (0.5)}{\log(0.85)}[/tex]
[tex]x=4.26[/tex]
Approximately the number of years it will take is 4 years.
