Question

Question

Use the table to answer the 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

$4919.85
$4919.85

$4,810
$4,810

$4,920

Answer 1

To calculate the value of the personal watercraft after two years, we start with the initial amount of $6,500 and apply the depreciation rate of 13% each year.

The common ratio for depreciation is: \[ 1 - 0.13 = 0.87 \]

Now, we can calculate the value for each year:

• After Year 0 (initial value): \[ \text{Value} = 6500 \]

• After Year 1: \[ \text{Value} = 6500 \times 0.87 = 5655 \]

• After Year 2: \[ \text{Value} = 5655 \times 0.87 \]

Now, let's calculate this: \[ 5655 \times 0.87 = 4928.85 \]

When rounded to the nearest whole dollar, the amount is: \[ \text{Value after Year 2} = 4929 \]

Now, let’s review the options provided:

• $4,919
• $4,919.85
• $4,810
• $4,920

The closest option to our calculated value of $4,928.85 is $4,920.

Thus, the personal watercraft will be worth $4,920 after two years.