Question

Brianna bought her car for $26,883. It is expected to depreciate an average of 15% each year during the first 2 years.

What will the approximate value of her car be in 2 years? Round answer to the nearest dollar. Do not include the units in your answer.

Answer 1

$22808.1

Explanation:

First, it is best to put this in a Geometric Sequence:

Aₙ = A₁ × rⁿ⁻¹

A₁ = $26,833

r = 85% or 0.85. This is because the 1st Value is $26,833, so that value will be 100%. Since the value is decreasing by 15% each year we remove 15% leading us to use 85% has our common ratio

Geometric Sequence: Aₙ = $26,833 × 0.85ⁿ⁻¹

Second, we plug in the value for n

In this geometric sequence, n is the number of years. Since we are doing 2 years, n = 2.

A₂ = $26,833 × 0.85²⁻¹

A₂ = $26,833 × 0.85

A₂ = $22808.1