Question

A car is purchased for $34,000. Each year it loses 25% of its value. After how many years will the car be worth $14,300 or less?

A) 3 years
B) 4 years
C) 5 years
D) 6 years

Answer 1

The car originally purchased for $34,000 will be worth $14,300 or less after 4 years. This is determined using the exponential decay formula for depreciation and solving for time.

Step-by-step explanation:

To determine after how many years a car bought for $34,000 will be worth $14,300 or less, considering it loses 25% of its value each year, we can use the formula for exponential decay, which is V = P(1 - r)^t, where V is the future value of the car, P is the original price, r is the rate of depreciation (as a decimal), and t is time in years.

Let's substitute the known values into the formula and solve for t:

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We get the following equation:

$14,300 = $34,000(1 - 0.25)^t

Solving for t logarithmically, t = log($14,300/$34,000) / log(0.75)

Calculating numerically:

t = log(0.420588) / log(0.75) ≈ log(0.420588) / -0.124939 = 3.364,

Since we want the full years, we'd round up to 4 years, because the car's value will dip below $14,300 during the fourth year.

The correct option is B) 4 years.