David M. Bressoud
Macalester College, St. Paul, MN
Bellingham, WA, May 20, 2006
This PowerPoint will be available at
www.macalester.edu/~bressoud/talks
The Schedule for the 2006 exam
Spring 2004: select problems for operational, alternate, and
overseas exams; for each exam there are 3 common problems, 3
AB only, 2 BC only, 1 AB/BC split
The Schedule for the 2006 exam
Spring 2004: select problems for operational, alternate, and
overseas exams; for each exam there are 3 common problems, 3
AB only, 2 BC only, 1 AB/BC split
Summer 2004: review 2nd drafts
The Schedule for the 2006 exam
Spring 2004: select problems for operational, alternate, and
overseas exams; for each exam there are 3 common problems, 3
AB only, 2 BC only, 1 AB/BC split
Summer 2004: review 2nd drafts
Fall 2004: review 3rd drafts
The Schedule for the 2006 exam
Spring 2004: select problems for operational, alternate, and
overseas exams; for each exam there are 3 common problems, 3
AB only, 2 BC only, 1 AB/BC split
Summer 2004: review 2nd drafts
Fall 2004: review 3rd drafts
Spring 2005: finalize the free-response problems
The Schedule for the 2006 exam
Spring 2004: select problems for operational, alternate, and
overseas exams; for each exam there are 3 common problems, 3
AB only, 2 BC only, 1 AB/BC split
Summer 2004: review 2nd drafts
Fall 2004: review 3rd drafts
Spring 2005: finalize the free-response problems
Summer 2005: review final version, especially in light of 2005
exam; review multiple choice exam
The Schedule for the 2006 exam
Spring 2004: select problems for operational, alternate, and
overseas exams; for each exam there are 3 common problems, 3
AB only, 2 BC only, 1 AB/BC split
Summer 2004: review 2nd drafts
Fall 2004: review 3rd drafts
Spring 2005: finalize the free-response problems
Summer 2005: review final version, especially in light of 2005
exam; review multiple choice exam
Fall 2005: check printers proofs of free response questions,
finalize the multiple choice problems
The Schedule for the 2006 exam
Spring 2004: select problems for operational, alternate, and
overseas exams; for each exam there are 3 common problems, 3
AB only, 2 BC only, 1 AB/BC split
Summer 2004: review 2nd drafts
Fall 2004: review 3rd drafts
Spring 2005: finalize the free-response problems
Summer 2005: review final version, especially in light of 2005
exam; review multiple choice exam
Fall 2005: check printers proofs of free response questions,
finalize the multiple choice problems
November-December 2005: chief reader and committee chair
check printers proofs of multiple choice exam
2002 AB2/BC2
The rate at which people enter an amusement park on a given day is modeled by the
15600
function E defined by
E t  
t
2
 24t  160

The rate at which people leave the same amusement park is modeled by the function
L defined by
9890
L t   2
t  38t  370


Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid for 9  t  23 , the hours during which the
park is open. At time t=9, there are no people in the park.
a)
How many people have entered the park by 5 PM (t=17)? Round answer to
the nearest whole number.
b)
The price of admission to the park is $15 until 5:00 PM (t=17). After 5:00
PM, the price of admission to the park is $11. How many dollars are
collected from admissions to the park on the given day? Round your answer
to the nearest whole number.
c)
d)
Let H t   9 E x   L x dx for 9  t  23 . The value of H(17) to
the nearest whole number is 3725. Find the value of H'(17) and explain the
meaning of H(17) and H'(17) in the context of the park.
t
At what time t, for 9  t  23 , does the model predict that the number of
people in the park is a maximum?
2000: AB4
Water is pumped into an underground tank at a constant rate of 8 gallons
per minute. Water leaks out of the tank at the rate of t  1
gallons per minute, for 0  t  120 minutes. At time t = 0, the tank
contains 30 gallons of water.
a)
b)
c)
d)
How many gallons of water leak out of the tank from time t = 0 to t
= 3 minutes?
How many gallons of water are in the tank at time t = 3 minutes?
Write an expression for A(t), the total number of gallons of water in
the tank at time t.
At what time t, for 0  t  120, is the amount of water in the tank a
maximum? Justify your answer.
The Source
On the average day during the summer months the rate that people enter a
particular amusement park at any time t (in hours) is estimated by the
function E(t). The rate that they leave is estimated by the function
L(t). Both E(t) and L(t) are given in hundreds of people per hour. The
park opens at 9:00 a.m. and stays open until 11:00 p.m.
E t  
a)
b)
c)
d)
e)
9.17
x  1 / 4   1
2
L t  
8
x  8  / 3  1
2
Graph y = E(t) and y = L(t) on the axes provided.
To the nearest hundred how many people have entered the park by
noon?
Let N(t) represent the number of hundreds of people in the park at
any time t. Write an expression for N(t).
At what time (to the nearest minute) is the largest number of people
in the park?
If each ticket costs $20, how much revenue is collected on an average
day? Express your answer to the nearest dollar.
The Source
On the average day during the summer months the rate that people enter a
particular amusement park at any time t (in hours) is estimated by the
function E(t). The rate that they leave is estimated by the function
L(t). Both E(t) and L(t) are given in hundreds of people per hour. The
park opens at 9:00 a.m. and stays open until 11:00 p.m.
E t  
a)
b)
c)
d)
e)
9.17
x  1 / 4   1
2
L t  
8
x  8  / 3  1
2
Graph y = E(t) and y = L(t) on the axes provided.
To the nearest hundred how many people have entered the park by
noon?
Let N(t) represent the number of hundreds of people in the park at
any time t. Write an expression for N(t).
At what time (to the nearest minute) is the largest number of people
in the park?
If each ticket costs $20, how much revenue is collected on an average
day? Express your answer to the nearest dollar.
The Source
On the average day during the summer months the rate that people enter a
particular amusement park at any time t (in hours) is estimated by the
function E(t). The rate that they leave is estimated by the function
L(t). Both E(t) and L(t) are given in hundreds of people per hour. The
park opens at 9:00 a.m. and stays open until 11:00 p.m.
E t  
a)
b)
c)
d)
e)
9.17
x  1 / 4   1
2
L t  
8
x  8  / 3  1
2
Graph y = E(t) and y = L(t) on the axes provided.
To the nearest hundred how many people have entered the park by
noon?
Let N(t) represent the number of hundreds of people in the park at
any time t. Write an expression for N(t).
At what time (to the nearest minute) is the largest number of people
in the park?
If each ticket costs $20, how much revenue is collected on an average
day? Express your answer to the nearest dollar.
The Source
On the average day during the summer months the rate that people enter a
particular amusement park at any time t (in hours) is estimated by the
function E(t). The rate that they leave is estimated by the function
L(t). Both E(t) and L(t) are given in hundreds of people per hour. The
park opens at 9:00 a.m. and stays open until 11:00 p.m.
E t  
a)
b)
c)
d)
e)
9.17
x  1 / 4   1
2
L t  
8
x  8  / 3  1
2
Graph y = E(t) and y = L(t) on the axes provided.
To the nearest hundred how many people have entered the park by
noon?
Let N(t) represent the number of hundreds of people in the park at
any time t. Write an expression for N(t).
At what time (to the nearest minute) is the largest number of people
in the park?
If each ticket costs $20, how much revenue is collected on an average
day? Express your answer to the nearest dollar.
The Source
On the average day during the summer months the rate that people enter a
particular amusement park at any time t (in hours) is estimated by the
function E(t). The rate that they leave is estimated by the function
L(t). Both E(t) and L(t) are given in hundreds of people per hour. The
park opens at 9:00 a.m. and stays open until 11:00 p.m.
E t  
a)
b)
c)
d)
e)
9.17
x  1 / 4   1
2
L t  
8
x  8  / 3  1
2
Graph y = E(t) and y = L(t) on the axes provided. Bad question - no calculus
To the nearest hundred how many people have entered the park by
noon?
Let N(t) represent the number of hundreds of people in the park at
any time t. Write an expression for N(t).
At what time (to the nearest minute) is the largest number of people
in the park?
If each ticket costs $20, how much revenue is collected on an average
day? Express your answer to the nearest dollar.
The Source
On the average day during the summer months the rate that people enter a
particular amusement park at any time t (in hours) is estimated by the
function E(t). The rate that they leave is estimated by the function
L(t). Both E(t) and L(t) are given in hundreds of people per hour. The
park opens at 9:00 a.m. and stays open until 11:00 p.m.
E t  
a)
b)
Same c)
question
d)
e)
9.17
x  1 / 4   1
2
L t  
8
x  8  / 3  1
2
Graph y = E(t) and y = L(t) on the axes provided.
To the nearest hundred how many people have entered the park by
noon?
Let N(t) represent the number of hundreds of people in the park at
any time t. Write an expression for N(t).
At what time (to the nearest minute) is the largest number of people
in the park?
If each ticket costs $20, how much revenue is collected on an average
day? Express your answer to the nearest dollar.
January 2001
The rate at which people enter an amusement park on a given day is approximated by the
function E defined by E t  
15000
. The rate at which people leave the same
t 2  24t  160
amusement park is approximated by the function L defined by L t  
9200
t 2  38t  370
Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid from 9:00 AM (t = 9), when the park
opens, until 11:00 PM (t = 23), when the park closes.
a)
b)
c)
d)
How many people have entered the park by noon (t = 12)? Round your answer to
the nearest whole person.
Let N(t) represent the number of people in the park at time t. Write an expression for
N(t) .
At what time t is the greatest number of people in the park?
The price of admission to the park is $20 until 5:00 PM (t = 17). After 5:00 PM, the
price of admission to the park is $15. Approximately how many dollars are collected
from admission to the park on a given day? Give your answer to the nearest dollar.
January 2001
The rate at which people enter an amusement park on a given day is approximated by the
function E defined by E t  
15000
. The rate at which people leave the same
t 2  24t  160
amusement park is approximated by the function L defined by L t  
9200
t 2  38t  370
Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid from 9:00 AM (t = 9), when the park
opens, until 11:00 PM (t = 23), when the park closes.
a)
b)
c)
d)
How many people have entered the park by noon (t = 12)? Round your answer to
the nearest whole person.
Let N(t) represent the number of people in the park at time t. Write an expression for
N(t) .
At what time t is the greatest number of people in the park?
The price of admission to the park is $20 until 5:00 PM (t = 17). After 5:00 PM, the
price of admission to the park is $15. Approximately how many dollars are collected
from admission to the park on a given day? Give your answer to the nearest dollar.
January 2001
The rate at which people enter an amusement park on a given day is approximated by the
function E defined by E t  
15000
. The rate at which people leave the same
t 2  24t  160
amusement park is approximated by the function L defined by L t  
9200
t 2  38t  370
Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid from 9:00 AM (t = 9), when the park
opens, until 11:00 PM (t = 23), when the park closes.
a)
b)
c)
d)
Better to use an interval:
9 ≤ t ≤ 23
How many people have entered the park by noon (t = 12)? Round your answer to
the nearest whole person.
Let N(t) represent the number of people in the park at time t. Write an expression for
N(t) .
At what time t is the greatest number of people in the park?
The price of admission to the park is $20 until 5:00 PM (t = 17). After 5:00 PM, the
price of admission to the park is $15. Approximately how many dollars are collected
from admission to the park on a given day? Give your answer to the nearest dollar.
January 2001
The rate at which people enter an amusement park on a given day is approximated by the
function E defined by E t  
15000
. The rate at which people leave the same
t 2  24t  160
amusement park is approximated by the function L defined by L t  
9200
t 2  38t  370
Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid from 9:00 AM (t = 9), when the park
opens, until 11:00 PM (t = 23), when the park closes.
a)
b)
c)
d)
How many people have entered the park by noon (t = 12)? Round your answer to
the nearest whole person.
Let N(t) represent the number of people in the park at time t. Write an expression for
N(t) .
At what time t is the greatest number of people in the park?
The price of admission to the park is $20 until 5:00 PM (t = 17). After 5:00 PM, the
price of admission to the park is $15. Approximately how many dollars are collected
from admission to the park on a given day? Give your answer to the nearest dollar.
January 2001
The rate at which people enter an amusement park on a given day is approximated by the
function E defined by E t  
15000
. The rate at which people leave the same
t 2  24t  160
amusement park is approximated by the function L defined by L t  
9200
t 2  38t  370
Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid from 9:00 AM (t = 9), when the park
opens, until 11:00 PM (t = 23), when the park closes.
a)
b)
c)
d)
How many people have entered the park by noon (t = 12)? Round your answer to
the nearest whole person.
Let N(t) represent the number of people in the park at time t. Write an expression for
N(t) .
At what time t is the greatest number of people in the park?
The price of admission to the park is $20 until 5:00 PM (t = 17). After 5:00 PM, the
price of admission to the park is $15. Approximately how many dollars are collected
from admission to the park on a given day? Give your answer to the nearest dollar.
March 2001
The rate at which people enter an amusement park on a given day is approximated by the
function E defined by E t  
15300
. The rate at which people leave the same
t 2  24t  160
amusement park is approximated by the function L defined by L t  
9200
t 2  38t  370
Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid for 9  t  23, the hours during which the
park is open.
a)
b)
c)
d)
How many people have entered the park by noon (t = 12)? Round your answer to
the nearest whole number. 2 pts
Let N(t) represent the number of people in the park at time t, for 9  t  23 . Write
an expression for N(t) . 2 pts
At what time t, for 9  t  23, is the greatest number of people in the park? 2 pts
The price of admission to the park is $20 until 5:00 PM (t = 17). After 5:00 PM, the
price of admission to the park is $15. Approximately how many dollars are collected
from admission to the park on a given day? Give your answer to the nearest dollar.
3 pts
March 2001
The rate at which people enter an amusement park on a given day is approximated by the
function E defined by E t  
15300
. The rate at which people leave the same
t 2  24t  160
amusement park is approximated by the function L defined by L t  
9200
t 2  38t  370
Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid for 9  t  23, the hours during which the
park is open.
a)
b)
c)
d)
e)
How many people have entered the park by noon (t = 12)? Round your answer to
the nearest whole number. 2 pts
Let N(t) represent the number of people in the park at time t, for 9  t  23 . Write
an expression for N(t) . 2 pts
At what time t, for 9  t  23, is the greatest number of people in the park? 2 pts
The price of admission to the park is $20 until 5:00 PM (t = 17). After 5:00 PM, the
price of admission to the park is $15. Approximately how many dollars are collected
from admission to the park on a given day? Give your answer to the nearest dollar.
3 pts
Find the maximum number of people in the park.
March 2001
The rate at which people enter an amusement park on a given day is approximated by the
function E defined by E t  
15300
. The rate at which people leave the same
t 2  24t  160
amusement park is approximated by the function L defined by L t  
9200
t 2  38t  370
Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid for 9  t  23, the hours during which the
park is open.
a)
b)
c)
d)
How many people have entered the park by noon (t = 12)? Round your answer to
the nearest whole number. 2 pts
Let N(t) represent the number of people in the park at time t, for 9  t  23 . Write
an expression for N(t) . 2 pts
At what time t, for 9  t  23, is the greatest number of people in the park? 2 pts
The price of admission to the park is $20 until 5:00 PM (t = 17). After 5:00 PM, the
price of admission to the park is $15. Approximately how many dollars are collected
from admission to the park on a given day? Give your answer to the nearest dollar.
3 pts
e) At what time is the number of people in the park rising fastest, and when is the
rate at which people are entering the greatest?
March 2001
The rate at which people enter an amusement park on a given day is approximated by the
function E defined by E t  
15300
. The rate at which people leave the same
t 2  24t  160
amusement park is approximated by the function L defined by L t  
9200
t 2  38t  370
Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid for 9  t  23, the hours during which the
park is open.
a)
b)
c)
d)
How many people have entered the park by noon (t = 12)? Round your answer to
the nearest whole number. 2 pts
Let N(t) represent the number of people in the park at time t, for 9  t  23 . Write
an expression for N(t) . 2 pts
At what time t, for 9  t  23, is the greatest number of people in the park? 2 pts
The price of admission to the park is $20 until 5:00 PM (t = 17). After 5:00 PM, the
price of admission to the park is $15. Approximately how many dollars are collected
from admission to the park on a given day? Give your answer to the nearest dollar.
3 pts
e) What is the average amount of time a person spends in the park?
July 2001
The rate at which people enter an amusement park on a given day is modeled by the
function E defined by
15300
E t   2
t  24t  160
The rate at which people leave the same amusement park is modeled by the function
L defined by
9200
L t   2
t  38t  370
Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid for 9  t  23 , the hours during which the
park is open.
July 2001
The rate at which people enter an amusement park on a given day is modeled by the
function E defined by
15300
E t   2
t  24t  160
The rate at which people leave the same amusement park is modeled by the function
L defined by
9200
L t   2
t  38t  370
Put denominators inside parentheses!
Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid for 9  t  23 , the hours during which the
park is open.
a)
How many people have entered the park by noon (t=12)? Round answer to
the nearest whole number.
b)
Let H t   9 E x   L x dx for 9  t  23 . Explain the meaning of
H(12) and H'(12) in the context of the amusement park.
c)
At what time t, for 9  t  23, is the number of people in the park greatest?
d)
The price of admission to the park is $20 until 5:00 PM (t=17). After 5:00
PM, the price of admission to the park is $15. According to this model, how
many dollars are collected from admissions to the park on the given day?
Round your answer to the nearest dollar.
t
a)
How many people have entered the park by noon (t=12)? Round answer to
the nearest whole number.
b)
Let H t   9 E x   L x dx for 9  t  23 . Explain the meaning of
H(12) and H'(12) in the context of the amusement park.
c)
At what time t, for 9  t  23, is the number of people in the park greatest?
d)
The price of admission to the park is $20 until 5:00 PM (t=17). After 5:00
PM, the price of admission to the park is $15. According to this model, how
many dollars are collected from admissions to the park on the given day?
Round your answer to the nearest dollar.
t
a)
How many people have entered the park by noon (t=12)? Round answer to
the nearest whole number. 2 pts
b)
Let H t   9 E x   L x dx for 9  t  23 . Explain the meaning of
H(12) and H'(12) in the context of the amusement park. 2 pts
c)
At what time t, for 9  t  23, is the number of people in the park greatest? 2 pts
d)
The price of admission to the park is $20 until 5:00 PM (t=17). After 5:00
PM, the price of admission to the park is $15. According to this model, how
many dollars are collected from admissions to the park on the given day?
Round your answer to the nearest dollar. 3 pts
t
a)
b)
c)
d)
How many people have entered the park by noon (t=12)? Round answer to
the nearest whole number. 2 pts -> 3 pts
Let H t   9 E x   L x dx for 9  t  23 . Explain the meaning of
H(12) and H'(12) in the context of the amusement park. 2 pts
Find value of H'(17).
At what time t, for 9  t  23, is the number of people in the park greatest? 2 pts
t
The price of admission to the park is $20 until 5:00 PM (t=17). After 5:00
PM, the price of admission to the park is $15. According to this model, how
many dollars are collected from admissions to the park on the given day?
Round your answer to the nearest dollar. 3 pts -> 1 pt
October 2001
The rate at which people enter an amusement park on a given day is modeled by the
15600
function E defined by
E t  
t
2
 24t  160

The rate at which people leave the same amusement park is modeled by the function
L defined by
9890
L t   2
t  38t  370


Both E(t) and L(t) are measured in people per hour and time t is measured in hours
after midnight. These functions are valid for 9  t  23 , the hours during which the
park is open. At time t=9, there are no people in the park.
a)
How many people have entered the park by 5 PM (t=17)? Round your
answer to the nearest whole number.
b)
The price of admission to the park is $15 until 5:00 PM (t=17). After 5:00
PM, the price of admission to the park is $11. How many dollars are
collected from admissions to the park on the given day? Round your answer
to the nearest whole number.
c)
d)
Let H t   9 E x   L x dx for 9  t  23 . The value of H(17) to
the nearest whole number is 3725. Find the value of H'(17) and explain the
meaning of H(17) and H'(17) in the context of the amusement park.
t
At what time t, for 9  t  23 , does the model predict that the number of
people in the park is a maximum?
a) How many people have entered the park by 5 PM
(t=17)? Round answer to the nearest whole
number.
3 points: 2 pts for set-up (1 for correct limits, 1 for
correct integrand), 1 pt for answer

17
9
E t dt  6004 people
b) The price of admission to the park is $15 until 5:00
PM (t=17). After 5:00 PM, the price of admission
to the park is $11. How many dollars are collected
from admissions to the park on the given day?
Round your answer to the nearest whole number.
1 point: set-up only
$15   E t dt  $11   E t dt  $104048
17
9
23
17
or
$15  6004  $11  1271  $104041
c) Let H t   9 E x   L x dx for 9  t  23 .
The value of H(17) to the nearest whole number is
3725. Find the value of H'(17) and explain the
meaning of H(17) and H'(17) in the context of the
park.
t
3 points: 1 pt for H'(17) and 1 pt for each explanation
H ' 17   E 17   L 17   380.281 people/hour
H(17) is the number of people in the park at time t =
interpretation
17. H'(17) is the rate at which the number of people
in the park is changing. The number of people in the
park is decreasing at a rate of approximately 380 implication
people per hour.
Ambiguous
•The rate of the number of people at 5 PM
•The rate at which people enter/leave (enter and leave, enter or leave) at 5 PM
•The rate at which people stay at 5 PM
•This compares the rates at which people enter and leave at 5 PM
Acceptable
•The rate of change of the number of people at 5 PM
•The rate at which the number of people is changing at 5 PM
•The net rate of change of the number of people at 5 PM
•The difference between rate of entering and rate of leaving at 5 PM
Unacceptable
•Any reference to average rate of change
•Any reference to something occurring over an interval of time
•The number of people leaving the park at 5 PM
•The rate which people leave the park at 5 PM
d) At what time t, for 9  t  23 , does the model
predict that the number of people in the park is a
maximum?
2 points: 1 pt for recognizing that this occurs when
E(t) – L(t) = 0, 1 pt for finding the answer: t =
15.794 or t = 15.795 hours after midnight.
AB average: 3.13, SD = 2.82
grade
percentage
Range of score
Average score
5
4
3
18.0%
23.0%
26.3%
6–9
4–6
1–4
7.39
5.00
2.43
BC average: 4.90, SD = 2.81
grade
percentage
Range of score
Average score
5
4
3
43.3%
16.3%
21.6%
6–9
5–6
2–5
7.46
5.30
3.40
1. When is the rate at which people are entering the
park greatest?
2. At what time is the total number of people in the
park increasing at the greatest rate?
3. What is the greatest number of people in the park
at any time?
4. How many people are in the park when it closes
at 11:00 PM?
5. What is the average amount of time each person
spends in the park?
Start with easier question: What if everyone stays
until 11:00 PM?
If someone enters at time t, they spend 23 – t hours
in the park. How many people enter at time t?
Start with easier question: What if everyone stays
until 11:00 PM?
If someone enters at time t, they spend 23 – t hours
in the park. How many people enter at time t?
Number of people who enter between time t
and time t  t is E t   t
E t   t  23  t  people hours spent in park
Start with easier question: What if everyone stays
until 11:00 PM?
If someone enters at time t, they spend 23 – t hours
in the park. How many people enter at time t?
Number of people who enter between time t
and time t  t is E t   t
E t   t  23  t  people hours spent in park
 E t 23  t t
i
i


23
9
E t 23  t dt people hours
Adjust for those who leave before 11:00 PM.

23
9
E t 23  t dt   L t 23  t dt  30382.933 people hours
23
9
Adjust for those who leave before 11:00 PM.

23
9
E t 23  t dt   L t 23  t dt  30382.933 people hours
23
9
Total number who enter the park is

23
9
E t dt  7275.553
Adjust for those who leave before 11:00 PM.

23
9
E t 23  t dt   L t 23  t dt  30382.933 people hours
23
9
Total number who enter the park is

23
9
E t dt  7275.553
Answer is
30382.933 people hours
 4.176 hours = 4 hours, 11 minutes
7275.553 people
APCentral
at apcentral.collegeboard.com
SIGMAA TAHSM (Special Interest Group of the
MAA, Teaching Advanced High School
Mathematics)
at www.maa.org/SIGMAA/tahsm/
This PowerPoint presentation
at www.macalester.edu/~bressoud/talks