Question

Will purchased a car for $21,000. If V = 21,000(0.85)x gives the value of the car after x years, how many years will it take for the car to be worth half of its original value?

Answer 1

4 years will it take for the car to be worth half of its original value.

Explanation:

Given : Will purchased a car for $21,000. If
`V = 21,000(0.85)^x` 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 :

`V = 21,000(0.85)^x` gives the value of the car after x years.

The car to be worth half of its original value i.e.
`V=(21000)/(2)=10500`

`10500 = 21000(0.85)^x`

`(10500)/(21000)=(0.85)^x`

`0.5=(0.85)^x`

Taking log both side,

`\log (0.5)=x\log(0.85)`

`x=(\log (0.5))/(\log(0.85))`

`x=4.26`

Approximately the number of years it will take is 4 years.