Question

The table below represents the cost, in hundreds of thousands of dollars, for operating a factory for x hours. The data is modeled by the function .

hours 1 2 3 4
cost 110 156 203 259 332

Approximately how many hours of operation will result in a cost of $310,000?

4.25
4.5
4.75
5.0

Answer 1

First convert $310{,}000 to the table's units: 310 (hundreds of thousands). Between 4 and 5 hours the cost goes from 259 to 332, an increase of 73. The fraction of that increase needed is (310 − 259)/73 = 51/73 ≈ 0.699, so the time is about 4 + 0.699 ≈ 4.70 hours. Closest choice: 4.75.