Question

A construction company purchases a bulldozer for $60,000. Each year the value of the bulldozer depreciates by 20% of its value in the preceding year. Let Vₙ be the value of the bulldozer in the n th year. (Let n=1 be the year the bulldozer is purchased.) Find a formula for Vₙ.

Answer 1

To find a formula for Vₙ, the value of the bulldozer in the n th year, we can use the given information. The bulldozer depreciates by 20% of its value in the preceding year. Let's start with the initial value V₀ = $60,000.

Step-by-step explanation:

To find a formula for Vₙ, the value of the bulldozer in the nth year, we can use the given information. The bulldozer depreciates by 20% of its value in the preceding year. Let's start with the initial value V₀ = $60,000.

To find V₁, the value in the first year, we need to subtract 20% of V₀ from V₀. This can be written as V₁ = V₀ - 0.20 * V₀. Simplifying this equation gives us V₁ = V₀ * (1 - 0.20).

To find V₂, the value in the second year, we again subtract 20% of V₁ from V₁. This can be written as V₂ = V₁ - 0.20 * V₁. Simplifying this equation gives us V₂ = V₁ * (1 - 0.20).

We can continue this pattern to find a general formula for Vₙ. Each year, we subtract 20% of Vₙ₋₁ from Vₙ₋₁. This can be written as Vₙ = Vₙ₋₁ - 0.20 * Vₙ₋₁. Simplifying this equation gives us Vₙ = Vₙ₋₁ * (1 - 0.20).