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

$4,810
$4,810

$4,920
$4,920

$4,919
$4,919

$4919.85

Answer 1

To find the value of the personal watercraft after two years with a 13% annual depreciation, we can apply the common ratio of the geometric sequence, which is 0.87 (as the value decreases to 87% of its previous value each year).

Starting with the initial value of $6,500:

1. After Year 1:
   Value at Year 1 = $6,500 * 0.87
   Value at Year 1 = $5,655

2. After Year 2:
   Value at Year 2 = $5,655 * 0.87
   Value at Year 2 = $4,920.85

Now rounding this to the nearest whole dollar gives us:

Value after 2 years = $4,921

Looking at the options provided, the closest value is $4,920.

Thus, the answer is:

$4,920.