1. An analyst is assessing a DM's utility function for annual total vehicle travel time TVTT^ann,, in units of [10⁶ veh-hrs], ranging from 0 to 20, and wishes to use a function:

() = (20 ), 0 < tvttann < 20

20

The analyst has determined that the DM is indifferent between Alternative A and Alternative B:

Alternative A: Probability 0.3of incurring 0 [10⁶ veh-hrs]

Probability 0.7of incurring 20 [10⁶ veh-hrs]

Alternative B: Probability 1.0of incurring 5 [10⁶ veh-hrs]

What would you use for the DM's utility function? Show your work.