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

$4,919
$4,919

$4,920
$4,920

$4919.85
$4919.85

$4,810
$4,810
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Answer 1

To calculate the value of the personal watercraft after two years, we can use the given depreciation rate of 13%. The common ratio for the geometric sequence is 0.87, meaning that the value after each year is multiplied by 0.87.

1. First Year: The initial value is $6,500. After one year: \[ \text{Value after Year 1} = 6500 \times 0.87 = 5,655 \]

2. Second Year: Now, we take the value after the first year and apply the same depreciation: \[ \text{Value after Year 2} = 5655 \times 0.87 \] Calculating this: \[ 5655 \times 0.87 = 4,919.85 \]

Rounding to the nearest whole dollar, the value after two years is approximately $4,920.

Therefore, the correct answer is: $4,920.