Question

Mr. Rich bought a truck for $45,000. Each year, the truck depreciates by 5%. Part A: Write an equation to represent the situation (use ^ for an exponent). Part B: What is the value of the truck after 10 years? Round to the nearest hundredth?

A) $26,730.92
B) $26,217.38
C) $29,169.03
D) $29,835.59.

Answer 1

The equation representing the situation is V = P(1 - r)^t. The value of the truck after 10 years is approximately $26,730.92.

Step-by-step explanation:

Part A: To represent the situation, we can use the formula for exponential decay:

V = P(1 - r)^t

Where:

• V is the value of the truck after t years
• P is the initial value of the truck, which is $45,000
• r is the rate of depreciation, which is 5% or 0.05
• t is the number of years, which we can plug in later

Part B: To find the value of the truck after 10 years, we substitute the values into the formula:

V = $45,000(1 - 0.05)^10

V ≈ $26,730.92

Therefore, the value of the truck after 10 years is approximately $26,730.92 (Option A).