To determine whether the decreasing value of the car can be modeled by a linear decay function or an exponential decay function, let's analyze the data provided:
- The value of the car decreases from $54,000 in Year 0 to $51,840 in Year 1.
- The value decreases to $49,766 in Year 2.
- It continues decreasing to $47,776 in Year 3 and $45,865 in Year 4.
Calculating the percentage change each year:
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From Year 0 to Year 1: \[ \frac{51,840 - 54,000}{54,000} = \frac{-4,160}{54,000} \approx -0.077 \] which is approximately -7.7%.
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From Year 1 to Year 2: \[ \frac{49,766 - 51,840}{51,840} = \frac{-2,074}{51,840} \approx -0.040 \] which is approximately -4.0%.
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From Year 2 to Year 3: \[ \frac{47,776 - 49,766}{49,766} = \frac{-1,990}{49,766} \approx -0.040 \] which is approximately -4.0%.
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From Year 3 to Year 4: \[ \frac{45,865 - 47,776}{47,776} = \frac{-1,911}{47,776} \approx -0.040 \] which is approximately -4.0%.
The percentage decreases are not constant, but they are relative to the value of the car each year. This indicates that the decay is not linear (where a constant amount is subtracted each year), but rather follows an exponential decay pattern, where a constant percentage is deducted based on the value at the beginning of each year.
Thus, the correct response is:
exponential decay function; the value decreases by 4% per year, which is a constant percent rate of change.
1 answer