Which statement is true based on the given data?
The option d: "During the first three years Trevor owned the desk, the resale value was less than the cost. Then it exceeded the cost after year 3."
Analysis of Antique Desk Resale Value
Understanding the Data:
Trevor purchased an antique desk, and the net value of the desk is determined by subtracting the purchase cost from the resale value. An exponential function f, as shown in the table, represents the net value of the desk for different years after Trevor bought it.
The table provides the following information:
| x |
f(x) |
| 0 |
-37 |
| 1 |
-26 |
| 2 |
-13 |
| 3 |
0 |
| 4 |
15 |
| 5 |
32 |
Analysis:
Based on the data provided, we can observe the following trends:
- The net value starts at -37 when x is 0 and gradually increases over time.
- The net value becomes positive after 3 years (x=3).
- The net value continues to increase as x increases.
Conclusion:
From the analysis, we can determine that during the first three years Trevor owned the desk, the resale value was less than the cost he paid for it. This is evident from the negative net values in the table for x=0, x=1, and x=2. After year 3, the resale value exceeded the cost, as indicated by the positive net values for x=3, x=4, and x=5.
In conclusion, the correct statement based on the data is that during the first three years Trevor owned the desk, the resale value was less than the cost. Then it exceeded the cost after year 3.