Graph Transformations
Applying Exponential Equations
Initial Amount, Growth Factor, and Growth Rate
Writing Exponential Functions
Compound Interest
100

Name the transformations occurring: 

f(x) = 2x-3

What is a vertical translation down 3 units?

100
The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. Find the number population of the town after 9 years.
Approximately 42,640 people
100

Use y = 250(1.2)t What is the initial?

What is 250

100
Write an exponential growth function to model the situation. A population of 422,000 increases by 12% each year.
What is f(x) = 422,000(1.12)^x
100

Kendra deposited $80 in a savings account earning 5% interest, compounded annually. To the nearest cent, how much will she have in 2 years?

$88.20

200

Name the transformations occurring: 

f(x)=100(0.5)x

What is vertical stretch by factor of 100?

200
$1,200 is invested at an annual rate of 3.2%. How much money will the account have after 12 years?
$1751.21
200

Use y = 250(1.2)t What is the growth factor?

What is 1.2

200
The population of Baconburg starts off at 20,000, and grows by 13% each year. Write an exponential growth model and find the population after 10 years.
What is f(10) = 20,000(1.13)^10 and population of 67,891
200

Tisha has $50 in a savings account that earns 4% interest, compounded quarterly. To the nearest cent, how much interest will she earn in 3 years?

$56.34

300

Name the transformations occurring:

 f(x)=(1.4)x-2

What is a horizontal translation 2 units right?

300

The population in the town of Deersburgh is presently 42,500. The town has been growing at a steady rate of 2.7%. What will the population of the town be in 5 years?

Approximately 48,556 People

300

Use y = 250(1.2)t What is the growth rate?

What is 20%

300
The Hippityhoppity bunny decided to have a family reunion at the Magic Forest every 5 years. During the second reunion the family discovered that the number of family members was 154 and was growing at an annual rate of 3.2%. Write an equation to model the growth of the bunny family.
What is f(x) = 154(1.032)^x
300

Lex has $1,780.80 in his savings account that he opened 6 years ago. His account has an annual interest rate of 6.8% compounded annually. How much money did Lex use to open his savings account?

$1,200

400

Name the transformations occurring: 

f(x) = -3x-1

What is a reflection across the x-axis and a vertical translation down 1 unit?

400
The value of a car was $22,000 when it was purchased. They car depreciates at a rate of 19% per year. How much will the car be worth in 8 years?
$4,076.64
400

y = 9.8(1.35)t What is the growth factor?

What is 1.35

400
The fish in The Magic Forest Lake were declining at an annual rate at 1.5%. Their current number is estimated at 2500. Write an equation to model the decreasing number of fish.
What is y = 2500(.985)^x
400

Steve invests a $2,807 in a 401k account with a fixed annual interest rate of 9% that is compounded continuously. After 13 years, what is the account balance?

$9,044.13

500

Name the transformations: 

f(x) = -0.5 (1.25)x+3

What is a reflection over the x-axis, vertical compression of factor 0.5, and horizontal translation 3 units left? 

500
The value of a stock when purchased is $10 a share. However, over the past 5 days the price went down at a constant rate of 4%. How much is the stock worth now?
$8.15
500

y = 9.8(1.35)t What is the growth rate?

What is 35%

500
The squid in The Magic Forest Lake were declining at an annual rate at 5.5%. Their current number is estimated at 50,000. Write an equation to predict the number of squid in the lake in 10 years.
What is f(10) = 50000(.945)^10 and 28,398 squid
500

Daniel invests a lump sum of money in a savings account with a fixed annual interest rate of 5% that is compounded continuously. After 7 years, the account balance reaches $5,676.27. How much was initially  invested?

$4,000

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