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 $4919.85, $4,920,$4,810, $4,919

Answer 1

To find the value of the personal watercraft after two years, we use the formula for geometric sequences. The value after each year is obtained by multiplying the previous year's value by the common ratio (0.87 in this case).

1. Initial value (year 0): $6,500
2. Value after year 1: \( 6500 \times 0.87 = 5655 \)
3. Value after year 2: \( 5655 \times 0.87 = 4920.05 \)

Now rounding to the nearest whole dollar, we get \( \approx 4920 \).

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