Exponential Functions

Is it Growth Or Decay?

Tables

Word Problems

Equations

Random

100

When something depreciates, does it grow or decay?

decay

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

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

100

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

x y

__ __

x y

0 5

1 15

2 45

3 135

100

What do exponential functions look like?

Curved lines

200

y=67(0.676767)^x

Is the graph growing or decaying?

decaying

200

Find the slope

x y

1 6

2 12

3 24

4 48

Create a function for the table

y=3(2)^x

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

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

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

x y

0 99

1 33

2 11

decay

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

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

300

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

x y

__ __

x y

0 900

1 450

2 225

3 112.5

300

What are the key components of exponential functions? Describe them

a= initial value (when x=0)

b= growth or decay rate

400

y= 6(3.5)^x

Is the graph growing or decaying?

growing

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

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

400

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

x y

__ __

x y

0 -900

1 -90

2 -9

3 -0.9

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

Create a word problem that represents a decay rate.

Answers may vary

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

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

500

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

x y

__ __

x y

0 200

1 -100

2 50

3 -25

500

When is Ms Kieu's last day here

Next Thurs/Friday