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Growth or Decay?
Applying Exponential Equations
Initial Amount, Growth Factor, and Growth Rate
Writing Exponential Functions
Geometric Sequences
100
Is the following growth or decay: f(x) = 2^x
What is growth
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

Is the following a Geometric sequence? 300, 290, 280, 270, ...

No, this is arithmetic 

200
Is the following growth or decay: f(x)=100*(0.5)^x
What is decay
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

Is the sequence geometric? If so, identify the common ratio. 1/2,  1/8,  1/32,  1/128, ....

Yes, common ratio is 1/4

300

Is the following growth or decay: f(x)= 100*(1-.4)^x

What is decay

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 42, 499 People
300

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

1.35

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

Write the formula for the geometric sequence:

  8, 24, 72, 216, ...

f(n) = 8(3)^n-1

OR

f(n) = 2.7(3)^n

400

What is the percent change for the following: f(x) = 7 (0.94)^x

6% Decay 

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

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

20% growth

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

What is the 5th term in the geometric sequence:

9072, 1512, 252, ...  

7

500

What is the percent change for the following: f(x) = -350 (1.05)^x

5% growth

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

Write the formula for the geometric sequence:

15, 30, 60, 120, ...


f(n) = 15(2)^n-1

OR

f(n) = 7.5(2)^n