Question

A new automobile is purchased for $20,000. If V = 20,000(0.8)x, gives the car’s value after x years, about how long will it take for the car to be worth $8,200?

Answer 1

Explanation:

We can start by setting up an equation to solve for x, the number of years it will take for the car to be worth $8,200:

8200 = 20000(0.8)^x

Dividing both sides by 20,000, we get:

0.41 = 0.8^x

Taking the logarithm of both sides (using any base, as long as we're consistent), we get:

log(0.41) = log(0.8^x)

Using the property of logarithms that allows us to bring down the exponent as a coefficient, we get:

log(0.41) = x log(0.8)

Dividing both sides by log(0.8), we get:

x = log(0.41) / log(0.8)

Using a calculator, we find:

x ≈ 5.92

Therefore, it will take about 5.92 years for the car to be worth $8,200.