Exponential Functions Jeopardy

Writing Exponential Functions

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

200

The stock of Apple starts off at 20,000, and grows by 6% monthly. Write an exponential growth model for the function

What is f(x) = 20,000(1.005)^12t

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)⁵

400

The fish in The Magic Forest Lake were increasing at an annual rate at 1.5% semiannually. Their current number is estimated at 2500. Write an equation to model the number of fish.

What is y = 2500(1.0075)^2x

500

The amount in a CD is increasing by compounding 3% monthly. The initial amount put in the CD was 250. Write an equation to find the amount of money in the account.

f(x)=250(1.0025)^12x

Tables and Graphs

100

Make a table for the function f(x)=3^x

-2     -1    0     1     2

1/9   1/3   1    3      9

200

Graph the function f(x)=2^x

Teacher will check graphs

300

Graph the function f(x)=2^x

Teacher will check graphs

400

Write the function for this table:

x: -2    -1    0    1   2

y: 32    16   8    4    2

f(x)=8(1/2)^x

500

Write the function for this table:

x:  -2      -1     0     1       2

y:  1.75  3.5    7     14     28

f(x)=7(2)^x

Applying Exponential Equations

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

200

$1,200 is invested and compounded semiannually at a rate of 2%. How much money will the account have after 12 years?

$1524

300

The population in the town of Deersburgh is presently 42,500. The town has been growing at a steady rate of 3%. What will the population of the town be in 5 years?

Approximately 49,269 People

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

500

You invest $27,000 in a savings account that pays an annual interest rate of 1.8%. The savings account is set to compound quarterly. How much is in your account after 5 years? 

$29,536.74

Recursive and Explicit Formulas

100

Write the exponential function for this sequence:

2,4,6,8,10...

f(x)=2(2)^x

200

Write the recursive formula for this sequence:

3,6,12,24,48...

A(n)=2a(n-1)

a(1)=3

300

What is the explicit formula for this sequence:

3, 2, 4/3, 8/9, 16/27...

a(n)=3(2/3)^n-1

400

Write the recursive and explicit formula for this sequence:

1, 2.3, 5.29, 12.167...

Recursive: A(n)=2.3a(n-1)  A(1)=1

Explicit= 1(2.3)^n-1

500

Write the explicit formula and determine the 8th term:

9, 3, 1/3, 1/9...

Explicit: A(n)=9(1/3)^n-1

8th term: 1/243

Misc.

100

Is the following growth or decay: f(x) = 2^x

What is growth

200

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

What is decay

300

Identify the y-intercept and constant ratio of the function f(x)=3(1.5)^x

y-int= 3 or (0,3)

constant ratio= 1.5

400

What are the domain and range of the function?

f(x)=1/2(9)^x

Domain- ARN 

Range- y>0

500

Define asymptote and identify the asympotote of this function: f(x)=5(6)^x

Asymptote is a line that a function gets closer and closer to but does not touch.

y=0