Aria buys a new car for $36,000. She learns that every year her car will depreciate in value by 15%. This means that each year her car will be worth 85% of what it was the previous year. Aria tracks how much her car is worth over time.

Question

Create a sequence that describes the worth of Aria’s car each year for 8 years. (Write answers in the form or 2,000 or 1,567.87)

Answer 1

Aria's car depreciates by 15% each year, meaning it retains 85% of its value each subsequent year. We can calculate the value of the car for each of the 8 years using the formula:

\[ \text{Value after } n \text{ years} = \text{Initial Value} \times (0.85)^n \]

In this case, the initial value is $36,000. We can compute the value for each year:

1. Year 0:
   \[ 36000 \times (0.85)^0 = 36000 \]

2. Year 1:
   \[ 36000 \times (0.85)^1 = 36000 \times 0.85 = 30600 \]

3. Year 2:
   \[ 36000 \times (0.85)^2 = 36000 \times 0.7225 = 26010 \]

4. Year 3:
   \[ 36000 \times (0.85)^3 = 36000 \times 0.614125 = 22050.50 \]

5. Year 4:
   \[ 36000 \times (0.85)^4 = 36000 \times 0.52200625 = 18852.24 \]

6. Year 5:
   \[ 36000 \times (0.85)^5 = 36000 \times 0.4437053125 = 15973.43 \]

7. Year 6:
   \[ 36000 \times (0.85)^6 = 36000 \times 0.376889453125 = 13587.28 \]

8. Year 7:
   \[ 36000 \times (0.85)^7 = 36000 \times 0.32098400640625 = 11591.54 \]

9. Year 8:
   \[ 36000 \times (0.85)^8 = 36000 \times 0.27249015344665625 = 9809.67 \]

Now combining these values, we have the sequence representing the worth of Aria's car each year for 8 years:

• Year 0: $36,000.00
• Year 1: $30,600.00
• Year 2: $26,010.00
• Year 3: $22,050.50
• Year 4: $18,852.24
• Year 5: $15,973.43
• Year 6: $13,587.28
• Year 7: $11,591.54
• Year 8: $9,809.67

Thus, the sequence of the car's worth over 8 years is:

• $36,000.00
• $30,600.00
• $26,010.00
• $22,050.50
• $18,852.24
• $15,973.43
• $13,587.28
• $11,591.54
• $9,809.67