REAL-LIFE PROBLEM
Old Faithful is a popular attraction at Yellowstone National Park, because the geyser
produces eruptions that are fairly predictable. When tourists visit Old Faithful, they will
see a sign that indicates an estimated time that the geyser will next erupt.
On average, Old Faithful erupts every 17 minutes, and each eruption lasts about 1
minute long.
a. The pattern over time has caused park rangers to develop predictable eruption
times using a(n) _______________ sequence.
b. In minutes, give the pattern of the first 5 eruptions: ______________________
c. Write an equation to represent the pattern of eruptions. ____________________
d. You are a park ranger and start your shift at 8 AM and work until 11 AM.
Estimate how many eruptions will see you during your shift? Show your work or
explain how you found your answer.
e. During your shift, the first eruption you put on the sign for tourists is 8:05 am.
Using your formula and your estimate of the number of eruptions, what is the last
time you will put on the sign for tourists. Show your work or explain how you
found your answer.
http://www.geyserstudy.org/summaries/electronic_summary_2011.htm
http://www.scribd.com/doc/43722472/Real-Life-Example-of-Arithmetic-Pogression
Answer key:
a.
b.
c.
d.
e.
arithmetic sequence
17, 35, 53, 71, 89
a=17, d=18 an = 18n-1
3 hour shift, 180 min shift, 180/18 = 10 eruptions
Acceptable answers 11:04, 10:46
a10 = 18(10) – 1 = 179 minutes
(8:05 add 180 minutes or 3 hours to get 10:05, subtract 1 = 11:04)
a9 = 18(9) – 1 = 161 minutes
(161-120 = 41 minutes, 8:05 + 2 hours = 10:05 + 41 minutes = 10:46)