#### Solved Examples and Worksheet for Comparing Linear, Quadratic and Exponential Models

Q1Which of the following models represents the equation y = ax2 + bx + c?

A. Linear model
C. Exponential model
D. Cubic model

Step: 1
The equation y = ax2 + bx + c represents a quadratic model.
Q2Name the type of model that best fits the data collection: (- 1, - 1), (0, 1), (1, 3), (2, 5), (3, 7), (4, 9), (5, 11)

A. Linear model
B. Exponential model
D. Cubic model

Step: 1
Draw a scatter plot of the data.
Step: 2 Step: 3
From the graph, you can see that the points appear to lie on a line.
Step: 4
So, the type of model which best fits the data is a Linear model.
Correct Answer is :   Linear model
Q3Name the type of model suggested by the graph. A. Linear model
C. Exponential model
D. Cubic model

Step: 1
You can see that the graph is a straight line.
Step: 2
So, the type of model represents the graph is a Linear model.
Correct Answer is :   Linear model
Q4Name the type of model suggested by the graph. B. Cubic model
C. Linear model
D. Exponential model

Step: 1
You can see that the graph is an Exponential curve.
Step: 2
So, the type of model represents the graph is an Exponential model.
Correct Answer is :   Exponential model
Q5Name the model that the graph of y = 1.3(0.82)x represents.

A. Linear
B. Exponential growth
C. Exponential decay

Step: 1
Make a table of values and draw a scatter plot.
Step: 2 Step: 3 Step: 4
From the graph, you can see that the points appear to lie on an exponential curve.
Step: 5
As the x increases, then y decreases. So the graph of y = 1.3 (0.82)x represents an exponential decay.
Correct Answer is :   Exponential decay
Q6Tony has $500 in his bank account. The table shows the amount B available in the account after t years. Choose the model and its equation which best fits the situation.  Time(t) 0 1 2 3 4 5 Balance($) (B) 500 530 560 590 620 650

A. Linear; B = 500 + 30t
B. Exponential; B = 500 (1.06)t
D. Linear; B = 500 + 6t

Step: 1
Draw a scatter plot of the data. Step: 2
You can see that the graph is a straight line.
Step: 3
Find two points on the line such as (0, 500) and (1, 530).
Step: 4
m = y2 -y1x2 -x1 = 530 - 5001 - 0 = 30
[Find slope of the line.]
Step: 5
Using a y-intercept of 500 and a slope of m = 30, you can write an equation of the line.
Step: 6
B = mt + b
[Write slope-intercept form.]
Step: 7
B = 30t + 500
[Substitute 500 for b and 30 for m.]
Step: 8
So, the linear model B = 500 + 30t fits the data.
[Replace b with 500 and m with 30.]
Correct Answer is :   Linear; B = 500 + 30t
Q7Name the type of model that best fits the data collection shown.
 x -1 0 1 2 3 y -3 -1 1 3 5

B. Exponential model
C. Cubic model
D. Linear model

Step: 1
Draw a scatter plot of the data.
Step: 2 Step: 3
From the graph, it is observed that the points appear to lie on a line.
Step: 4
Therefore, the model that best fits the data is a linear model.
Correct Answer is :   Linear model
Q8Which of the following equation represents an exponential model?
A. y = 2 - 3x
B. y = (2.1)x + 4
C. y = 4 + 2x2
D. y = 3(5.02)x

Step: 1
The equation y = 3(5.02)x is of the form y = c(1 + r)x.
Step: 2
So, the equation y = 3(5.02)x represents an exponential model.
Correct Answer is :   y = 3(5.02)x
Q9Name the type of model that best fits the data collection shown.
 x -2 -1 0 1 2 3 y -0.88 -0.5 0 1 3 7

A. Cubic model
B. Linear model
C. Exponential model

Step: 1
Draw a scatter plot of the data.
Step: 2 Step: 3
From the graph, it is observed that the points appear to lie on an exponential curve.
Step: 4
Therefore, the model that best fits the data is an exponential model.
Correct Answer is :   Exponential model
Q10Which of the following equation represents an exponential model?
A. y = 8(1.14)x
B. y = 3 + 4x2
C. y = 2x3 + 5
D. y = 4 - x

Step: 1
The equation y = 8(1.14)x is of the form y = c(1 + r)x.
Step: 2
So, the equation y = 8(1.14)x represents an exponential model.
Correct Answer is :   y = 8(1.14)x
Q11Which of the following equation represents a linear model?
A. y = 2(7.08)x
B. y = 3x + 4
C. y = 4x3 - 3
D. y = 1 - 3x2

Step: 1
The equation y = 3x + 4 is of the form y = mx + b.
Step: 2
So, the equation y = 3x + 4 represents a linear model.
Correct Answer is :   y = 3x + 4
Q12Which of the following equation represents a quadratic model?
A. y = - 2x3 + 1
B. y = 4x2 - 7
C. y = 8(3.26)x
D. y = -2x - 3

Step: 1
The equation y = 4x2 - 7 is of the form y = ax2 + bx + c.
Step: 2
So, the equation y = 4x2 - 7 represents a quadratic model.
Correct Answer is :   y = 4x2 - 7
• Function