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