Quiz 2-v4
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School
University of Toronto *
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Course
135
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
7
Uploaded by UltraRoseSeal55
Q1 Quiz #2 - 11:10am-12:00pm
0 Points
You need to be in-person
in tutorial otherwise it won't be graded. Your TA will take attendance in tutorial.
You only have 1 attempt
. Once you submit the quiz, you won't be able to see the questions or your answers until all the quizzes have been graded.
You need to complete all the questions, upload your answer to Q2.2 and submit the quiz by NOON
. The quiz will lock-up after that.
You are allowed
to:
Use a non-programmable calculator
Access Desmos or Geogebra
Access the textbook
Access your notes
Ask your TA if you have a question
You are not allowed
to: Watch videos (even course videos)
Use any internet resource not listed above
Communicate with anyone, except your TA
Q1.1 Tutorial Section
0 Points
My tutorial section is:
TUT0501
!
TUT0502
!
TUT0503
!
TUT0504
"
TUT0505
!
Q1.2 In-Person
0 Points
Q2 Racing cars
3 Points
A car's acceleration (in km/h
) depends on how much gasoline is pumped into the combustion chamber (in cm
), according to the following table:
Alternatively, the car's acceleration can be thought of as depending on the angle of the acceleration pedal (in degrees), according to TUT0505
!
TUT0506
!
TUT0507
!
TUT0508
!
TUT0509
!
TUT0510
!
TUT0511
!
TUT0512
!
TUT0513
!
I am writing this quiz in-person in the tutorial section selected
above.
!
I am writing this quiz online. I have an accommodation and have
notified my TA or Course Coordinator beforehand.
!
None of the above.
!
2
3
acceleration
gasoline
∣
∣
0
0
10000
5
20000
7
30000
15
40000
25
50000
40
60000
65
the following table.
Q2.1 Rate of Change
1 Point
From the options below, select the best estimate for the rate of change of the amount of gasoline in the combustion chamber as a function of the pedal angle when the pedal is at a 24
angle.
Q2.2 Explanation
2 Points
Explain your choice on Q2.1. Your answer should include the calculations as well a written explanation of your thought process.
No files uploaded
Q3 Tree and Rain
2 Points
Assume that the growth of a tree depends on how much water they can absorb through rain as in the graph below.
pedal angle
acceleration
∣
∣
0
0
4
20000
8
30000
12
42000
16
48000
20
52000
24
56000
∘
2 cm
/degree
!
3
5 cm
/degree
!
3
667 cm
/degree
!
3
1000 cm
/degree
!
3
#
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The next graph describes how much water was falling in that forest throughout the month.
We want to know when during the month the tree was growing the fastest. For that, we have to find the critical points for the tree growth as a function of time.
Select all the critical points:
Day 5
Day 10
Day 15
Day 20
Day 25
Q4 Bacteria
2 Points
The number of bacteria in a Petri dish grows rapidly, but then runs out of food and dies out quickly.
Which of the following families of models will the most appropriate for this situation?
Q5 Max
2 Points
Consider the function in the graph below.
Day 30
Quadratic polynomial: !
y
=
ax
+
2
bx
+
c
Logistic model: !
y
=
1 +
ae
−
bx
c
Exponential model with limit: !
y
=
a
(
1
−
e
)
−
bx
Bell-shaped curve: !
y
=
e
−
b
(
x
−
a
)
2
y
=
f
(
x
)
Q5.1 Max
1 Point
Then the maximum
of for is attained at
Q5.2 Min
1 Point
Then the minimum
of for is attained at
f
(
x
)
0
≤
x
≤
D
!
x
= 0
!
x
=
A
!
x
=
B
!
x
=
C
!
x
=
D
f
(
x
)
0
≤
x
≤
D
!
x
= 0
!
x
=
A
!
x
=
B
!
x
=
C
!
x
=
D
UNGRADED
Quiz #2 - Friday 11:10am-12:00pm
STUDENT
$
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STUDENT
Test Student
TOTAL POINTS
- / 9 pts
QUESTION 1
Quiz #2 - 11:10am-12:00pm
0 pts
1.1
Tutorial Section
0 pts
1.2
In-Person
0 pts
QUESTION 2
Racing cars
3 pts
2.1
Rate of Change
1 pt
2.2
Explanation
2 pts
QUESTION 3
Tree and Rain
2 pts
QUESTION 4
Bacteria
2 pts
QUESTION 5
Max
2 pts
5.1
Max
1 pt
5.2
Min
1 pt