Introduction to Exponential Functions

Growth or Decay

Exponential growth is looks like a curve increasing (gets higher) left to right. Exponential decay looks like a curve decreasing (gets smaller) left to right.

Multiple Choice

Is the pictured graph growth or decay?

• Growth

• Decay

• I don't know yet.

Multiple Choice

Is the pictured graph growth or decay?

• Growth

• Decay

• I don't know yet.

How can I tell if it is growth or decay in an equation?

When b > 1 it is growth (1 + r). When b < 1 then it is decay (1 - r).

Multiple Choice

What type of function is y = 7(5/4)^x?

• Exponential Growth
• Exponential Decay
• Linear
• None of the above

Multiple Choice

Which the following graphs shows an exponential decay equation?

Multiple Choice

In exponential decay problems, the decay value is always....

• More than zero, but less than 1

• Less than zero

• Greater than 1

• Whatever you want it to be

Multiple Choice

What type of function is f(x)=2(1/7)^x ?

• Exponential Growth
• Linear
• Exponential Decay
• None of the Abovee

Multiple Choice

What is the domain of the function?

• 1.567

• y > -5

• $$\left(-\infty,\infty\right)$$

• $$\left(-\infty,\ 2\right]$$

Multiple Choice

What is the y-intercept of this function?

• (0,0)

• (0,1)

• (-3,0)

• (0,-3)

Graphing

Graph the equation: $$y=3\left(2\right)^x$$

Graphing

Graph the equation: $$y=4\left(\frac{1}{2}\right)^x$$

Graphing

Graph the equation: $$y=3^x$$

Graphing

Graph the equation: $$y=2^x$$

Multiple Choice

Classify the following graph.

• Exponential Growth

• Exponential Decay

• Logarithmic

Multiple Choice

Classify the following graph.

• Exponential Growth

• Exponential Decay

• Logarithmic

Multiple Choice

What is the asymptote of this function:
 f(x) = 2^x-1 + 3

• x = 1
• x = -1
• y = 3
• y = - 3

Multiple Choice

Does the following represent growth or decay?

y=1/2(3)^x+2

• Growth

• Decay

Multiple Choice

What is the y-intercept of the function?

• 2

• 3

• 1

• -2

Graphing

Determine the y-intercept and asymptote for the following exponential function.

Hint: for the asymptote , just put a dot on where it would be!

$$y=2^x$$

Hotspot

Determine the y-intercept and asymptote for the following exponential function.

Hint: for the asymptote , just click which dot it would be, BE CAREFUL on this one!

Hotspot

Determine the y-intercept and asymptote for the following exponential function.

Hint: for the asymptote , just click which dot it would be, BE CAREFUL on this one!

Dropdown

The graph of an exponential function is shown on the grid. Which dashed line is an asymptote for the graph?

Select answer

Graphing

Determine the y-intercept and asymptote for the following exponential function.

Hint: for the asymptote , just put a dot on where it would be!

$$g\left(x\right)=5\left(\frac{1}{2}\right)^x$$

Graphing

Graph the following function:

Hint: Don't forget to move the asymptote line!

$$g\left(x\right)=4\left(\frac{1}{4}\right)^x-7$$

Multiple Choice

Does the function represent exponential growth or decay?

$$y=\frac{1}{8}\left(5\right)^x$$  

• Decay

• Growth

Multiple Choice

Identify the horizontal asymptote of the exponential function:

$$y=3\left(\frac{1}{2}\right)^x$$  

• y=3

• y=1/2

• x=3

• y=0

Multiple Choice

Describe the transformation on

$$y=2\left(4\right)^x$$  when if becomes  $$y=2\left(4\right)^{\left(x-5\right)}$$  

• Down 5

• Right 5

• Left 5

• Up 5

Multiple Choice

Describe the transformation on  $$y=\frac{1}{4}\left(3\right)^x$$  when it becomes  $$y=\frac{1}{4\ }\left(3\right)^x-9$$  

 

• Down 9

• Left 9

• Right 9

• Up 9

Multiple Choice

Identify the horizontal asymptote for the exponential function: $$y=\frac{1}{4}\left(3\right)^x-9$$  

• y = 0

• y = 3

• y = -9

• No Horizonal Asymptote

Multiple Choice

$$y=5\left(\frac{1}{3}\right)^{\left(x-1\right)}$$  

Identify the horizontal asymptote for the exponential function:

• y = 0

• x = -1

• y = -1

• y = 1

Poll

Would you rather.....

get $1000 a day for a year or penny that doubles every day for a month (day1 - 1 penny, day 2 - 2 pennies, day 3 - 4 pennies, etc. )?

• $1000 a day for a year

• penny that doubles for 30 days

Open Ended

Take a sheet of paper and fold it into half.

Fold it a second time, and a third time.

A sheet of paper is about 0.1 mm thick

If you fold paper 20 times how thick do you think it will be?

An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.

For example, exponential functions can be used to calculate changes in population, loan interest charges, bacterial growth, radioactive decay or the spread of disease.

Multiple Choice

Write the following in Exponential Form

6

• 6¹

• 1⁶

• 6

Multiple Choice

How would you represent 6⁵ ?

• $$5\cdot6$$

• $$6\cdot5$$

• $$6\cdot6\cdot6\cdot6\cdot6$$

• $$5\cdot5\cdot5\cdot5\cdot5$$

Multiple Choice

Rewrite 36 as 6 to some power

• $$6^1$$

• $$6^2$$

• $$6^3$$

• $$6^4$$

Fill in the Blank

$$\ 6^2=6^x\ \ Can\ you\ figure\ out\ what\ is\ x\ equals\ to?$$

Fill in the Blank

$$\ 2^5=2^x\ \ Can\ you\ figure\ out\ what\ is\ x\ equals\ to?$$

Multiple Choice

$$25^x=25^9$$

• 25

• 5

• 9

• 1

Multiple Choice

Solve for x:
(-3)^x = (-3)¹³

• 13
• -3
• x + 13
• x -13

Multiple Choice

8^3x = 8⁶

• x=2

• x=3
• x=18

• x=12

Multiple Choice

Rewrite 8 as 2 to some power.

• $$2^{16}$$  

• $$2^5$$  

• $$2^3$$  

• $$16^2$$  

Multiple Choice

$$8=2^x\ \ \ What\ is\ x?$$

• 8

• 2

• 3

• 1

Multiple Choice

Sovle for x:
$$5^x=25$$

• x = 1

• x = 2

• x = 25

• x = 5

Multiple Choice

Rewrite 49 as 7 to some power

• $$7^1$$

• $$7^2$$

• $$7^3$$

• $$7^4$$

Multiple Choice

Solve for x: $$7^{-x}=49$$

• x = 1
• x = -1
• x = 2
• x = -2

Fill in the Blank

Solve: $$4^{2p-3}=4^5$$