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 use the given formula to set up an equation and solve for x:

V = 20,000(0.8)x

where V is the value of the car after x years.

We want to find x when the value of the car is $8,200, so we set V equal to 8,200 and solve for x:

8,200 = 20,000(0.8)x

Dividing both sides by 20,000:

0.41 = 0.8x

Taking the natural logarithm of both sides:

ln(0.41) = x ln(0.8)

Dividing both sides by ln(0.8):

x = ln(0.41) / ln(0.8)

Using a calculator:

x ≈ 6.11

Therefore, it will take about 6.11 years for the car to be worth $8,200.