Exponential Function Review

Exponential Function Review

The Basics

• the a is the initial value

• the b is the constant ratio(multiplier)

• b> 1 = growth

• b< 1 = decay

• what are the domain and range?

Growth and Decay

• the rate

   $\pm$  1 is called the growth or decay factor

• x stands for time

• y stands for the new amount

Open Ended

Separate these equations into linear and exponential functions:

 $a:\ y=\ 4-2x$   $b:\ y=\ \frac{3}{4}x+\ 12$   $c:\ y=\ 3\left(2\right)^x$   $d:\ y=\ -5\ +\ 3^x$  

Open Ended

 $y=\ 60\left(\frac{1}{3}\right)^x$  

Evaluate the function and fill in the table:

Open Ended

A population of 6 gerbils doubles every 4 months. Write a function to show this growth.

Open Ended

 $y=\ 6\left(2\right)^x$  

How many gerbils would there be in 5 years (60 months)? Use the function given. 

Multiple Choice

What is the equation that represents the exponential function in the image below?

• y=3(½)^x
• y=3(2)^x
• y=(2)^x
• y=2(3)^x

Multiple Choice

What kind of transformation is represented?

• up 1 unit
• left 1 unit
• right 1 unit 
• down 1 unit

Multiple Choice

What is the asymptote of y = 2^x ?

• y = 0

• x = 0

Open Ended

Write an exponential function for the table

Open Ended

How can you tell from an equation if an exponential function is showing growth or decay?

Open Ended

 $f\left(x\right)\ =\ 20,000\left(0.75\right)^x$  This function shows a town that had an original population of ________ and is decreasing by _____ percent each year. 

Open Ended

A family buys a house for $165,000 and it increases in value by 4% each year. What will the value for the house be in 5 years?