Question

Suppose a new car that costs $25,000 depreciates by 12% each year. In about how many years will the car be worth $15,000? Use the equation 15,000 = (25,000)(0.88)x and round the value of x to the nearest year

Answer 1

X=log(15,000÷25,000)÷log(0.88)
x=3.9=4years

Answer 2

4 years.

Explanation:

Given : A new car that costs $25,000 depreciates by 12% each year.

To Find: In about how many years will the car be worth $15,000?

Solution:

Principal = $25000

Rate of decrease = 12%

Amount = $15000

Equation:
`15,000 = (25,000)(0.88)^x`

x will give the years in after which car value will be $15000

So,
`15,000 = (25,000)(0.88)^x`

`(15000)/(25000)=(0.88)^x`

`0.6=(0.88)^x`

`3.99603=x`

Thus in about 4 years car value will be $15,000.