Use the table to answer the question.

Question

Year 0 1 2
Amount ($) 6,500 5,655 ?

Townes bought a personal watercraft for $6,500. If it depreciates in value by 13% each year, the situation can be modeled using a geometric sequence with a common ratio of 0.87, which is started in the table. How much will the personal watercraft be worth after two years? Round the answer to the nearest whole dollar.(1 point)
Responses

$4,920
$4,920

$4,919
$4,919

$4,810
$4,810

$4919.85

Answer 1

To find the value of the personal watercraft after two years, we can use the formula for calculating the value after depreciation, which follows a geometric sequence.

Given:

1. Initial value (Year 0) = $6,500
2. Depreciation rate = 13%, which means the common ratio \( r = 1 - 0.13 = 0.87 \).

We can calculate the value for Year 1 and Year 2 as follows:

• Year 1: \[ \text{Value at Year 1} = \text{Initial value} \times r = 6500 \times 0.87 = 5,655 \]

• Year 2: \[ \text{Value at Year 2} = \text{Value at Year 1} \times r = 5655 \times 0.87 \] We can compute this: \[ 5655 \times 0.87 = 4,919.85 \]

Rounding $4,919.85$ to the nearest whole dollar gives us \( 4,920 \).

Thus, the value of the personal watercraft after two years is $4,920.