Question

A new car is purchased for $ 34 , 000 $34,000 and over time its value depreciates by one half every 5.5 years. How long, , would it take for the value of the car to be $ 1 , 000 $1,000?

Answer 1

Step-by-step explanation:

We can use the following formula to find the value of an asset that is depreciating at a constant rate over time:

V = P * (1/2)^(t/h)

where:

V = current value of the asset

P = initial value of the asset

t = time elapsed (in years)

h = half-life of the asset's value

In this case, we know that:

P = $34,000

V = $1,000

h = 5.5 years

Substituting these values into the formula, we get:

$1,000 = $34,000 * (1/2)^(t/5.5)

Dividing both sides by $34,000, we get:

(1/34) = (1/2)^(t/5.5)

Taking the natural logarithm of both sides, we get:

ln(1/34) = (t/5.5) * ln(1/2)

Solving for t, we get:

t = (5.5 / ln(1/2)) * ln(1/34)

Using a calculator, we get:

t ≈ 25.28

Therefore, it would take approximately 25.28 years for the value of the car to depreciate to $1,000.