Final answer:
To estimate the machine's worth after 12 years, we calculate the annual depreciation and subtract it from the machine's value after 2 years. The annual depreciation is $130 per year, and after 10 more years, the machine's value is $640, which does not match the given options. Hence, we cannot provide a correct answer without additional information.
Step-by-step explanation:
The question deals with the depreciation of a machine's value over time, and requires us to determine the machine's worth after 12 years given its worth after 2 years and 5 years. To solve this, we can assume a linear depreciation over time for simplicity since the exact method of depreciation is not provided. First, find the annual depreciation rate by taking the difference in the machine's value after 2 years ($1940) and after 5 years ($1550) and dividing it by the number of years between these two points in time (5 years - 2 years = 3 years).
The annual depreciation is \(($1940 - $1550) / (5 - 2) = $390 / 3 = $130\) per year. Using this annual depreciation, we can calculate the value after 12 years by subtracting the total depreciation from the initial value after 2 years. Total depreciation after 10 more years (from year 2 to year 12) will be \($130 \times 10 = $1300\). Thus, the value after 12 years would be \($1940 - $1300 = $640\), which does not match any of the given options.