Question

Carl bought a truck for $37,000 and the truck depreciates at 8.5% per year. What will the value of the truck be in 4 years? How long will it take the truck to have a value less than $10,000 ?

Answer 1

To find the value of the truck in 4 years, use the formula for exponential decay. It will take approximately 9 years for the value of the truck to be less than $10,000.

Step-by-step explanation:

To find the value of the truck in 4 years, we can use the formula for exponential decay:

V = P(1 - r)^t

Where:

• V is the final value
• P is the initial value
• r is the decay rate
• t is the time in years

Plugging in the values, we have:

V = $37,000(1 - 0.085)^4

Solving this equation, the value of the truck in 4 years will be approximately $26,698.98

To find how long it will take for the truck to have a value less than $10,000, we can set up the equation:

$10,000 = $37,000(1 - 0.085)^t

Solving for t, we get t ≈ 9.05

Therefore, it will take approximately 9 years for the value of the truck to be less than $10,000.