Old Faithful Old Faithful is a geyser in Yellowstone National Park named for its regular eruption pattern. Past data indicated that the average time between eruptions is 1 hr 35 m. Suppose rangers log the first eruption on a given day at 12 : 57 am. Using a 1 = 57 , write a prediction formula for the sequence of eruption times that day in terms of the number of minutes after midnight. At what time of day (e.g., 7 : 15 am) is the 10 th eruption expected to occur? At what time of day is the last eruption expected to occur?
Old Faithful Old Faithful is a geyser in Yellowstone National Park named for its regular eruption pattern. Past data indicated that the average time between eruptions is 1 hr 35 m. Suppose rangers log the first eruption on a given day at 12 : 57 am. Using a 1 = 57 , write a prediction formula for the sequence of eruption times that day in terms of the number of minutes after midnight. At what time of day (e.g., 7 : 15 am) is the 10 th eruption expected to occur? At what time of day is the last eruption expected to occur?
Solution Summary: The author explains the formula for sequence of eruptions times that day in terms of number of minutes after midnight, if the first eruption is at a_1=57, and the average time between eruption
Old Faithful Old Faithful is a geyser in Yellowstone National Park named for its regular eruption pattern. Past data indicated that the average time between eruptions is
1
hr
35
m.
Suppose rangers log the first eruption on a given day at
12
:
57
am. Using
a
1
=
57
, write a prediction formula for the sequence of eruption times that day in terms of the number of minutes after midnight.
At what time of day (e.g.,
7
:
15
am) is the
10
th eruption expected to occur?
At what time of day is the last eruption expected to occur?
The graph of the function f in the figure below consists of line segments and a quarter of a circle. Let g be the function given by
x
g(x) = __ f (t)dt. Determine all values of a, if any, where g has a point of inflection on the open interval (-9, 9).
8
y
7
76
LO
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
2 3
♡.
-1
-2
3
-4
56
-5
-6
-7
-8
Graph of f
4 5
16
7
8
9 10
The areas of the regions bounded by the graph of the function f and the x-axis are labeled in the figure below. Let the function g be
C
defined by the equation g(x) = [* f(t)dt. What is the maximum value of the function g on the closed interval [-7, 8]?
17
y
Graph of f
00
8
76
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3-2-1
-2
702
4
1
21
3 4
568
-4
-5
--6
-7
-8
x
5
6
7
8
9 10
17
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