Worksheet: Intersections of Exponential Functions with the Coordinate Axes

Q1:

The population of a country was 22 million people at the end of 2010. Since then, the population has increased by yearly. Determine the population of the country at the end of 2023. Give your answer in units of millions, correct to two decimal places.

Q2:

What is the point of intersection of the -axis and the graph of the function ?

• A
• B
• C
• D

Q3:

What is the point of intersection of the -axis and the graph of the function ?

• A
• B
• C
• D

Q4:

For what values of is the function increasing on its domain?

• A
• B
• C
• D

Q5:

Find the domain and range of , and determine whether it is an increasing function or a decreasing function.

• Adomain, range, decreasing on its domain
• Bdomain, range, increasing on its domain
• Cdomain, range, increasing on its domain
• Ddomain, range, decreasing on its domain

Q6:

Determine whether the function is increasing or decreasing.

• Bdecreasing on its domain
• Cincreasing on its range
• Dincreasing on its domain

Q7:

Suppose that .

Evaluate .

Evaluate .

Evaluate .

Evaluate .

Q8:

The curve with equation is the image of the curve with equation under reflection in which axis?

• A -axis
• B -axis

Q9:

The curve with equation is the image of the curve with equation under reflection in which axis?

• A -axis
• B -axis

Q10:

The graph shows the two functions and defined for . Both are decaying at a rate of .

What is the ratio of ?

What is the ratio of ?

Suppose that and with . How do and compare if at some point ?

• A
• B
• C
• D

Q11:

Find the domain and range of , and determine whether it is an increasing function or a decreasing function.

• Adomain, range, increasing on its domain
• Bdomain, range, decreasing on its domain
• Cdomain, range, decreasing on its domain
• Ddomain, range, increasing on its domain

Q12:

Find the point of intersection of the graph of with the straight line .

• A
• B
• C
• D
• E

Q13:

Consider an exponential function with base . For which values of is the function decreasing?

• A
• B
• C
• D