Old Faithful is a geyser in Yellowstone National Park named for its regular eruption pattern. Past data indicates that the average time between eruptions is 1h 35m.

(a) Suppose rangers log the first eruption on a given day at 12:57 am. Using a₁ = 57, write a prediction formula for the sequence of eruption times that day in terms of the number of minutes after midnight.
(b) At what time of day (e.g., 7:15 am) is the 10th eruption expected to occur?
(c) At what time of day is the last eruption expected to occur?