Name: ____________________________
Practice:
Exponential Functions
1.
x
-2
-1
0
1
y
128
32
8
2
c. Next = Now ____________
a. Initial Value:
b. Growth/Decay Factor:
d. y=____________________
e. Growth/Decay Rate:
Starting at ____________
2.
x
1
2
3
4
y
6
18
54
162
c. Next = Now ____________
a. Initial Value:
b. Growth/Decay Factor:
d. y=____________________
e. Growth/Decay Rate:
Starting at ____________
3.
x
0
1
2
3
y
4
.96
.2304
.055296
c. Next = Now ____________
a. Initial Value:
b. Growth/Decay Factor:
d. y=____________________
e. Growth/Decay Rate:
Starting at ____________
4. Given the following data from a large mouth bass population in a
local pond to the right, find the exponential equation that models
this situation. Let 0 represent the year 1970.
YEAR
POPULATION
1970
200
1971
300
1972
450
1973
675
YEAR
POPULATION
2000
5
2001
6
2002
7.2
2003
8.64
5. The population of a state from 2000 to 2003 is recorded in the table
below. What percent was the population growing by each year?
6. Write the equation of the exponential function modeled by each graph. (Hint: Make a table)!
a.
b.
7. (Review) Write an equation and Now-Next Rule for each function. (Hint, it may or may not be
exponential!)
x
y
-2
12
-1
3
0
0.75
1
0.1875
Comparing Linear and Exponential Functions
1. Lena has been offered a job with two salary options. The first option is modeled by the function
f(x) = 500x + 31,000. The second option is represented by the function g(x) = 29,000(1.04) x after x
years.
a. Make two tables to compare her salary for the first five years.
Option 1:
Option 2:
b. For which years would option 1 be a better choice?
c. For which years would option 2 be a better choice?
State the type (Linear, Exponential Growth, or Exponential Decay) of function and write an explicit
(y=___) function and recursive (Next=Now ___ SA____) to model each.
2.
3.
4.
𝑥
1
2
𝑓(𝑥)
9
3
3
4
1
1/3
Type: _____________________
Type: _____________________
Type: _____________________
Explicit: ___________________
Explicit: ___________________
Explicit: ___________________
Recursive: _________________
Recursive: _________________
Recursive: _________________
Starting at: ______
Starting at: ______
Starting at: ______
5.
6.
7. A population of bacteria in a
kitchen sponge is tripling every
hour. There are 100 bacteria at
the start.
Type: _____________________
Type: _____________________
Type: _____________________
Explicit: ___________________
Explicit: ___________________
Explicit: ___________________
Recursive: _________________
Recursive: _________________
Recursive: _________________
Starting at: ______
Starting at: ______
Starting at: ______
8.
x
y
-1
9.
x
y
20
-3
9
0
40
-2
12
1
80
-1
15
2
160
0
18
10.
x
y
-4
20
-3
10
-2
5
-1
2.5
Type: _____________________
Type: _____________________
Type: _____________________
Explicit: ___________________
Explicit: ___________________
Explicit: ___________________
Recursive: _________________
Recursive: _________________
Recursive: _________________
Starting at: ______
Starting at: ______
Starting at: ______
11.
x
y
1
1
2
3
3
9
4
27
12. A population of 350 rabbits 13.
is doubling each year.
There were 1,500 trees in a
forest. Each year,
are left.
!
!
of the trees
Type: _____________________
Type: _____________________
Type: _____________________
Explicit: ___________________
Explicit: ___________________
Explicit: ___________________
Recursive: _________________
Recursive: _________________
Recursive: _________________
Starting at: ______
Starting at: ______
Starting at: ______
14.
A cab company charges a 15.
$5.00 flat fee, and $0.50 per
mile.
16.
Type: _____________________
Type: _____________________
Type: _____________________
Explicit: ___________________
Explicit: ___________________
Explicit: ___________________
Recursive: _________________
Recursive: _________________
Recursive: _________________
Starting at: ______
Starting at: ______
Starting at: ______