Fd12 Ch6 Problem Set#2 6.3-6.4 PART A - WITHOUT GRAPHING TECHNOLOGY
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. The growth of a tree can be modelled by the function
h(t) = 2.3t – 0.45
where h represents the height in metres and t represents the time in years.
Approximately how long will it take the tree to grow 32 m tall?
A. 13 years
____
B. 14 years
C. 15 years
D. 16 years
2. Use a ruler to help you estimate the slope for a line that best approximates the data in the scatter
plot.
y
100
80
60
40
20
5
10
15
20
25
30
35
40
A. –1
____
x
45
B. 1
C. 2
D. 3
3. Use a ruler to help you estimate the slope for a line that best approximates the data in the scatter
plot.
20
y
18
16
14
12
10
8
6
4
2
2
A. –2
4
6
8
10
12
14
16
18
B. –1
x
C. 1
D. 2
____
4. Describe the characteristics of the trend in the data.
x
2
5
8
10
12
y
135
120
115
102
92
A. increasing
____
B. decreasing
14
85
17
78
C. constant
20
64
D. no trend
5. What kind of relationship might there be between the independent and dependent variables in this
scatter plot?
y
1000
900
800
700
600
500
400
300
200
100
1960
1970
1980
1990
2000
2010
x
A. linear
B. quadratic
____
C. cubic
D. none of the above
6. What kind of relationship might there be between the independent and dependent variables in this
scatter plot?
200
y
180
160
140
120
100
80
60
40
20
5
10
A. linear
B. quadratic
15
20
25
30
35
40
45
x
C. cubic
D. none of the above
____
7. The path of a shot put thrown at a track and field meet is modelled by the quadratic function
h(d) = –0.048(d2 – 20.7d – 26.28)
where h is the height in metres and d is the horizontal distance in metres.
Determine the height of the discus when it has travelled 10 m horizontally.
A. 6.2 m
____
B. 6.4 m
C. 6.6 m
D. 6.8 m
8. The average retail price of gas in Canada, from 1979 to 2008, can be modelled by the function
P(y) = 0.008y3 – 0.307y2 + 4.830y + 25.720
where P is the price of gas in cents per litre and y is the number of years after 1979.
Determine the average price of gas in 2002.
A. 68.8¢/L
B. 69.8¢/L
C. 70.4¢/L
D. 71.7¢/L
Short Answer
1. Use a ruler to help you estimate the y-intercept for a line that best approximates the data in the
scatter plot.
50
y
45
40
35
30
25
20
15
10
5
5
10
15
20
25
30
35
40
45
x
2. Determine the independent and dependent variables for the following relationship:
The latitude of a weather station is related to the mean temperature for April.
3. A snowboard company uses the relation
P(x) = 210x – 60x2
to model its profits. In the model, P is the profit in thousands of dollars and x is the number of
snowboards in thousands.
How much profit should the company expect if they manufacture 1800 snowboards?
4. The tide depth in a Pacific harbour from noon on March 1, 2012 to noon the next day can be
modelled by the cubic function
f(t) = 0.001t3 – 0.061t2 + 0.870t + 0.315
where f is the tide depth in metres and t is the number of hours after noon.
Determine the tide depth at 10:00 on the second day.
Problem
1. Ida hit a golf ball from the top of a hill. The height of the ball above the green can be modelled by
the regression equation
h(t) = –9.7t2 + 48.4t + 11.5
where h represent the height in metres and y represents the time in seconds.
a) Use your knowledge of polynomial functions to describe the curve of this function.
b) Determine the
y-intercept. What does it represent in this context? Show your work.
c) The roots of this equation are near t = –0.2 and t = 5.2. What do these points represent, if
anything?
Fd12 Ch6 Problem Set#2 6.3-6.4 PART A - WITHOUT GRAPHING TECHNOLOGY
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
ANS:
ANS:
ANS:
ANS:
B
C
B
B
5.
6.
7.
8.
ANS:
ANS:
ANS:
ANS:
B
C
B
D
SHORT ANSWER
1. ANS:
40
3. ANS:
$183 600
2. ANS:
Independent: latitude of a weather station
Dependent: mean temperature for April
4. ANS:
0.579 m
PROBLEM
1. ANS:
a) This is a quadratic function with a negative leading coefficient, so it must be a parabola that
opens down (it extends from quadrant III to quadrant IV). It will have a turning point that is a
maximum value, one y-intercept, and up to two x-intercepts.
b) The y-intercept is the value when t = 0.
h(t) = –9.7t2 + 48.4t + 11.5
h(0) = –9.7(0)2 + 48.4(0) + 11.5
h(0) = 11.5
This is the initial height of the ball.
c) The negative root does not have any meaning here since t is time and can only be positive. The
positive root is the time when the ball reaches the green.