Final answer:
The correct equation is option b, y = 24,599(0.7)^4, which models the car's value after depreciating 30% per year for 4 years. The value of the car after 4 years is approximately $5,905.16.
Step-by-step explanation:
The question is asking to calculate the value of a new car after it depreciates by 30% each year for 4 years.
Let's look at the provided equations and see which one accurately models this depreciation:
- y = 24,599(1.3)^4: This equation suggests an annual increase of 30%, which is incorrect.
- y = 24,599(0.7)^4: This equation represents the car's value decreasing by 30% each year. Since each year the car retains 70% of its value from the previous year, this is the correct model.
- y = 24,599(4)? : This equation does not make sense in this context.
- y = 24,599(4)1.3 : This equation seems to be a misunderstanding of the depreciation process.
So, option b is the correct equation. It calculates the car's value after 4 years by multiplying the initial price by 0.7 four times to account for four years of depreciation at 30% per year.
If we do the math for option b:
- y = 24,599 * (0.7)^4
- y = 24,599 * (0.2401)
- y = 5,905.1599
Therefore, the value of the car after 4 years would be approximately $5,905.16.