Initial Amount, Growth Factor, and Growth Rate
Applying Exponential Equations
Writing Exponential Functions
Geometric sequence
100

Use y = 250(1.2)t 

Growth or decay

Initial amount?

What is 

Growth and 250

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

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 this recursive or explicit

an= 5(an-1)

recursive

200

Use y = 250(1.2)t 

What is the growth factor?

What is the growth rate?

Factor is 1.2

Rate is 20%

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

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)x and population of 67,891

200

Recursive Formula or Explicit Formula

Find a35

Explicit Formula 

300

y = 9.8(0.82)t 

Growth or Decay?

Factor? 

Rate?

Decay

Factor 0.82

Rate 18%

300

Bao invested $510 in an account paying an interest rate of 3.7% compounded monthly. Assuming no deposits or withdrawals are made, how much money, would be in the account after 55 years?

$3890.45

300

Consider a savings account earning annual compound  modeled by the function s(x)=1000(1.035)x .

What does the 1.035 represent?

a) growth rate of 1.035

b) growth rate of 3.5%

c) growth rate of 35%

b) growth rate of 3.5%

300
What is the common ratio?

2, -10, 50, -250

r=-5

400

1500(1+0.05/4)4(6)

rate?

number of time compounded?

rate 5%

compounded quarterly n=4

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

Determine whether the function below is exponential growth or exponential decay, and find the percentage rate of change. f(x) =3.5(0.91)x
  

a) Exponential decay; 3.5%
b) Exponential growth; 9%
c) Exponential decay; 9%
d) Exponential growth; 3.5%


c) Exponential decay; 9%
400

Write the explicit formula for 

1, 6, 36, 216, ...

an=6x-1

500

y = 9800(1+.082/12)12(3) 

compounded?

initial amount?

rate?

compounded monthly 

initial amount 9800

rate 8.2%

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

Write a function that represents this table 

x        y

-2     0.25

-1     0.5

0      1

1      2

y= 2x

500

Write the explicit formula for the following sequence 

 2.4, 2.88, 3.456,...

an= 2.4(1.2)x-1

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