Exponential Functions

Is it Growth Or Decay?

100

When something depreciates, does it grow or decay?

decay

200

y=67(0.676767)^x

Is the graph growing or decaying?

decaying

300

x    y

0   99

1   33

2   11

decay

400

y= 6(3.5)^x

Is the graph growing or decaying?

growing

500

Create a word problem that represents a decay rate.

Answers may vary

Tables

100

Find the slope

x    y

0    40

1   20

2   10

3   5

Create a function for the table

y=40(0.5)^x

200

Find the slope

x    y

1   6

2   12

3   24

4   48

Create a function for the table

y=3(2)^x

300

Find the slope

x    y

1   48

2   16

3   5.33

4   1.77

Create a function for the table

y=144(0.33)^x

400

Find the slope

x    y

1   2000

2   3000

3   4500

4   13500

Create a function for the table

y=666.66(3)^x

500

Find the slope

x    y

1   6767

2   1353.4

3   270.68

4   54.136

Create a function for the table

y=33835(0.2)^x

Word Problems

100

1. Write an exponential function to model each situation. 

2. Find the value of the function after five years.

A baseball card bought for $50 increases 3% in value each year.

y= 50(1.03)^x

$58

200

A new car that sells for $18,000 depreciates 25% each year. 

1. Write a function that models the value of the car. 

2. Find the value of the car after 4 yr.

y=18000(0.75)^x

$5695

300

A new truck that sells for $29,000 depreciates 12% each year. 

1. Write a function that models the value of the truck. 2. Find the value of the truck after 7 yr.

y=29000(0.88)^x

$11,851

400

The bear population increases at a rate of 2% per year. There are 1573 bears this year. 

1. Write a function that models the bear population. 

2. How many bears will there be in 10 yr

y=1573(1.02)^x

$1,917

500

An investment of $75,000 increases at a rate of 12.5% per year. 

1. Find the value of the investment after 30 yr.

y=75,000(1.125)^x

$2,568,247

Equations

100

Create a table for y=5(3)^x

x     y

__  __

__  __

__  __

__  __

x     y

0     5   

1     15

2    45

3    135

200

Create a table for y=2(2.1)^x

x     y

__  __

__  __

__  __

__  __

x     y

0     2   

1     4.2

2    8.82

3    18.522

300

Create a table for y=900(0.5)^x

x     y

__  __

__  __

__  __

__  __

x     y

0     900   

1     450

2    225

3    112.5

400

Create a table for y= -900(0.1)^x

x     y

__  __

__  __

__  __

__  __

x     y

0     -900 

1     -90

2    -9

3    -0.9

500

Create a table for y=200(-0.5)^x

x     y

__  __

__  __

__  __

__  __

x     y

0     200

1     -100

2    50

3    -25

Random

100

What do exponential functions look like?

Curved lines

200

Finish the setting

"No more hiding, I'll be shinin' like I'm born to be
Cause we are hunters, voices strong, and I know I believe...."

We're goin' up, up, up, it's our moment
You know together we're glowin'
Gonna be, gonna be golden

300

What are the key components of exponential functions? Describe them

a=

b=

a= initial value (when x=0)

b= growth or decay rate

400

How do you turn a percent into a decimal?

Turn 9.67% into a decimal

Divide by 100 

9.67 / 100 = 0.0967

500

When is Ms Kieu's last day here

Next Thurs/Friday