6.3 Exponential Functions

6.3- Exponential Functions

Obj- To identify exponential functions and determine whether
they are growth or decay

Match

Warm-Up #1: Match the following graphs as linear or absolute value

Absolute Value

Linear

Neither

• Absolute Value

• Linear

• Neither

Match

Warm Up #2: Match the following

Linear

Absolute Value

Neither

• Linear

• Absolute Value

• Neither

● An exponential function is a nonlinear function of the

form where a _____ 0 b_____ 1, and b > 0.

● As the independent variable x change by a constant

amount, the dependent variable y is multiplied by a
constant factor, which means consecutive y-values form a
constant ratio.

Multiple Choice

Which of the following is an exponential function?

• $$f\left(x\right)=x^2$$

• $$f\left(x\right)=3x^3$$

• $$y=x^3$$

• $$f\left(x\right)=3^x$$

Examples- Does each table represent a linear or an exponential function? Explain.

Multiple Choice

Does the table represent a linear or exponential function?

• Linear

• Exponential

Multiple Choice

Does the table represent a linear of exponential function?

• Linear

• Exponential

Notes

Multiple Choice

What is the initial value in

$$y=25\left(4\right)^x$$  

• 25

• 4

• x

Multiple Choice

What is the growth or decay factor for the equation

$$f\left(x\right)\ =\ 25\left(4\right)^x$$  

• 25

• 4

Multiple Select

Select all the equations that represent exponential decay.

• $$y=\frac{1}{2}\left(4\right)^x$$

• $$y=4\left(\frac{1}{2}\right)^x$$

• $$y=80\left(1.4\right)^x$$

• $$y=60\left(0.7\right)^x$$

• $$y=3\left(0.6\right)^x$$

Multiple Select

Select the functions that are exponential growth.

• $$y=-2\left(3\right)^x$$

• $$f\left(x\right)=3\left(1.09\right)^x$$

• $$f\left(x\right)=4\left(\frac{1}{3}\right)^x$$

• $$y=0.5\left(\frac{3}{2}\right)^x$$

Multiple Choice

Classify the equation $$y\ =\ 120\left(\frac{1}{7}\right)^x$$  

• Growth

• Decay

• Linear

Multiple Choice

Identify the growth/decay value $$y\ =120\left(\frac{1}{7}\right)^x$$  

• 120

• $$\frac{1}{7}$$  

• x

Multiple Choice

Which graph represents exponential growth?

Multiple Choice

Which graph represents exponential decay?