To determine whether the decreasing value of the car can be modeled by a linear decay function or an exponential decay function, we need to analyze how the value changes each year.
From the table:
- Year 0: $54,000
- Year 1: $51,840
- Year 2: $49,766
- Year 3: $47,776
- Year 4: $45,865
To see if this represents a linear or exponential decay, we can look at the percentage decrease year over year:
-
From Year 0 to Year 1: \[ \text{Decrease} = 54,000 - 51,840 = 2,160 \] \[ \text{Percentage decrease} = \frac{2,160}{54,000} \times 100 \approx 4% \]
-
From Year 1 to Year 2: \[ \text{Decrease} = 51,840 - 49,766 = 2,074 \] \[ \text{Percentage decrease} = \frac{2,074}{51,840} \times 100 \approx 4% \]
-
From Year 2 to Year 3: \[ \text{Decrease} = 49,766 - 47,776 = 1,990 \] \[ \text{Percentage decrease} = \frac{1,990}{49,766} \times 100 \approx 4% \]
-
From Year 3 to Year 4: \[ \text{Decrease} = 47,776 - 45,865 = 1,911 \] \[ \text{Percentage decrease} = \frac{1,911}{47,776} \times 100 \approx 4% \]
In each calculation, the value decreases by approximately 4% every year. This indicates that the car's value is decreasing by a constant percentage, which is characteristic of exponential decay.
Therefore, the correct response is: exponential decay function; the value decreases by 4% per year, which is a constant percent rate of change.
1 answer