Exponential Functions

Creating Exponential Functions

100

x          y

0        256

1        64

2        16

3          4

4          1

y=256*(1/4)^x

200

x          y

0         6

1         30

2        150

3        750

y=6*5^x

300

x           y

0          3

1         30

2        300

3        3000

y=3*10^x

Growth and Decay

100

The price of a car that was bought for $10,000 has depreciated 10% every year.  Find the price 8 years later.

$4304.67

200

A town of 3200 grows at a rate of 25% every year.  Find the size of the city in 10 years.

29,802 people

300

A car was bought at $100,000.  Its value depreciates by 15% every year.  In what year was the value of the care $61,412.50?

Year 3

Geometric Sequences

100

1/4, 1/2, 1, 2, 4, 8, 16, ...

y=(1/4)*2^(n-1)

200

3, 9, 27, 81, 243, ...

y=3*(3)^(n-1)

300

625, 125, 25, 5, 1, 1/5, 1/25, ...

y=625*(1/5)^(n-1)

Exponential Transformations

100

Shift down 2

y=2^(x)-2

200

Shift left 3 and stretch by 4

y=4*2^(x+3)

300

Stretch by 3

Reflect over the x-axis

Right 1

Up 1

y=-3*2^(x-1)+1

Miscellaneous

100

What are the first five perfect squares?

0, 1, 4, 9, 16

200

What is the order for order of operations?

Parenthesis

Exponents

Multiplication and Division

Addition and Subtraction

300

What is the slope of a line?

m=(y₂-y₁)/(x₂-x₁)