Exponential Modeling and Comparing Exponential Functions

The linear function f(x) and the exponential function g(x) are graphed. 
The y-intercept for f(x) is ________ the y-intercept for g(x). 

• greater than
• less than
• equal to
• I do not know

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

The table represents f(x) while the graph represents g(x). 
The y-intercept of f(x) is _________ the y-intercept of g(x). 

• greater than
• equal to 
• less than 
• I do not know

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

The graph shows the function g(x). 
f(x)= 4(3)^{x
The growth factor of f(x) is ___________ the growth factor of g(x).} 

• less than
• greater than 
• equal to 
• I do not know

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Compounds A and B are used in an experiment. The equation f(x)= 800(1/2)^x represents the remaining amount of Compound A, in grams, after x minutes. The table shows the remaining amount of Compound B. 
What is the positive difference in the initial amounts of each compound?

• 300
• 200
• 100
• 500

Tags

CCSS.HSF.LE.A.2

The exponential function f(x) has an initial value of 4 with a growth factor of 2. 
A few values from the exponential function g(x) are shown below.
What is the positive difference between the y-intercept value of f(x) and g(x)? 

• 1
• -1
• 7
• 2

Tags

CCSS.HSF.LE.A.2

Challenge Question:
The linear function f(x) and the exponential function g(x) are graphed. Find the rate of change for both functions for the interval x= -1 and x=2.538. 
The rate of change for f(x) over the interval is _______ the rate of change of g(x) over the  same interval.

• greater than
• equal to
• less than 
• I do not know

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Challenge 2:
Which statement below describes the comparison of rate of change between the linear function f(x) and the exponential function g(x). 

• g(x) rate of change is ALWAYS greater than f(x) rate of change. 
• g(x) is NEVER greater than f(x) rate of change. 
• g(x) will eventually exceed the rate of change of f(x). 
• There is not enough information to compare the rate of change of f(x) to g(x).