Question

A construction company purchases a bulldozer for 160,000. 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

The formula for Vₙ is Vₙ = Vn-1 - 0.2Vn-1.

Step-by-step explanation:

Vₙ = Vn-1 - 0.2Vn-1

To find the formula for Vₙ, we need to consider the given information. We are told that the bulldozer depreciates by 20% of its value in the preceding year. Let's break it down step by step:

1. Since n=1 represents the year the bulldozer is purchased, the initial value of the bulldozer (V0) is $160,000.
2. In the first year (n=2), the bulldozer will depreciate by 20% of its initial value: V1 = V0 - 0.2V0 = $160,000 - $32,000 = $128,000.
3. For subsequent years, we can use the formula Vₙ = Vn-1 - 0.2Vn-1 to calculate the value in the n-th year.