Algebra 1: Exponentials Unit
Name ______________________________________
Period _______________ Date _________________
Review
I.
F-BF.1a Learning Target: I can identify
explicit and recursive patterns within a situation.
I can write an exponential function given a
situation.
2. The population of a sample of bacteria triples
every minute. If a is the initial population of the
a
sample, Kim believes the equation y  3  t 
can be used to find the population after t
minutes. Is Kim correct? Why or why not? If
not, make sure to include the correct equation in
your justification.
1. Jack is reviewing the change in the value of an
investment.
Investment
Time (years)
0
5
10
15
20
0.25
0.5
1
2
4
Circle one:
Investment ($100s)
Correct
or
Incorrect
Justification:______________________________
Write a function Jack can use to model this data.
What type of function is this? Why is this type of
function a good model for these data?
__________________________________________
__________________________________________
__________________________________________
__________________________________________
Function: _____________
Circle one:
Linear
or
Exponential
Justification:______________________________
__________________________________________
__________________________________________
__________________________________________
Algebra 1: Exponentials Unit Review
6/3/14
PUHSD Algebra Curriculum Team
II.
3.
c. Sketch the graph of h  x   3x  2 .
F-BF.3: Learning Target: I can infer how
the change in parameters a, b, h and k of an
exponential function transform the graph.
This graph below represents f  x   3x .
a. State the domain and range.
f  x   3x
How did the graph change?
How did the domain and range change?
b. Sketch the graph of g  x   3x .
d. Sketch the graph of k  x   3 x  2 .
How did the graph change?
How did the graph change?
How did the domain and range change?
How did the domain and range change?
Algebra 1: Exponentials Unit Review
06/03/14
PUHSD Algebra Curriculum Team
4.
Use a graphing calculator to determine how the
graph of y  5x would be affected if it was
changed to y  5x  2 ?
Change: _____________________________
III.
F-LE.1a Learning Target: I can prove that
linear functions grow by equal differences
over equal intervals, and that exponential
functions grow by equal factors over equal
intervals.
6.
x
h(x)
Common
Ratio
0
1
4
4
Part B: Based on that change, what type of function
is it?
a. The function changes by a constant rate, so
it is linear.
2
b. The function changes by a common ratio, so
it is exponential.
3
c. The function changes by constant rate, so it
is not linear.
Justification: _____________________________
__________________________________________
d. The function changes by a common ratio, so
it is not exponential.
__________________________________________
Algebra 1: Exponentials Unit Review
3
16
c. For equal intervals changing by 1 in the
independent variable, the corresponding
1
dependent value change by  .
4
d. For equal intervals changing by 1 in the
independent variable, the corresponding
1
dependent value change by a factor of .
4
x
y
2
64
Part A: How does the function represented in the
table change over equal intervals?
a. For equal intervals changing by 1 in the
independent variable, the corresponding
1
dependent value change by  .
4
b. For equal intervals changing by 1 in the
independent variable, the corresponding
1
dependent value change by a factor of .
4
1
5. Use a table to justify that y  3   is an
2
exponential function.
x
1
256
06/03/14
PUHSD Algebra Curriculum Team
V.
IV.
F-LE.2 Learning Target: I can write an
exponential function given a pattern, a set of
ordered pairs, a graph, or a description of an
exponential situation.
F-LE.3 Learning Target: I can compare
exponential growth to linear growth using
graphs and tables.
9. Which function appears to increase fastest as x
gets larger and larger, and will eventually
exceed the other function values?
7. What is the rule for the table below?
y
7200
f
g
6400
x
y
-2
2
-1
4
0
8
1
16
2
32
5600
4800
4000
3200
h
2400
1600
k
800
2
4
6
8
10
12
14
16
18
x
Answer:__________
8. A ball is dropped from a height of 50 feet. It
rebounds two-thirds of the height every time it hits
the ground.
Part A: Write a function that models the height of
the ball over time. (HINT: f ( x)  ab x )
Answer:__________
10.
Which function has greater value as x increases?
Use a table or graph to identify the function.
a. s( x)  10 x
b. q( x)  x3
50
Fee
t
c. r ( x)  16 x
d. t ( x)  2 x 2
e. v( x)  3x
Answer:__________
Function:________________
Part B: How would your function change if the
ball were “flat” and only rebounded one-eighth
of the height every time?
Algebra 1: Exponentials Unit Review
06/03/14
PUHSD Algebra Curriculum Team
VI.
F-LE.5 Learning Target: I can identify
common ratio (b) and initial value (a) of
y  ab x from a given context.
13.
11. Based on the change per unit interval, choose an
appropriate type of function to model the
situation. Justify your response.
A small company had an average monthly
electricity use of 8000 kilowatt-hours last
year. Their five-year plan calls for average
monthly electricity use to be reduced by 10%
each of the next five years. Identify the initial
value and the common ratio.
Population Decay of Bacteria
Time (hours)
Number of
Bacteria
0
90,000
1
27,000
2
8,100
3
2,430
4
729
Initial Value: ____________________
Common Ratio: __________________
Equation: _______________________
14.
a. Linear
b. Exponential
An initial investment of $10,000 grows at
per year. What function represents the value
of the investment after t years?
a. f (t )  10000(1.11)t
Answer:__________
Justification: _________________________
b.
f (t )  10000(1.11)t
c.
f (t )  10000(12)t
d.
f (t )  10000(0.11)t
_____________________________________
_____________________________________
_____________________________________
12. What is the common ratio of the following
exponential function? Justify your response.
x
y
0
1.5
1
6
2
24
3
96
4
384
5
1,536
Common Ratio:________
Justification: _________________________
_____________________________________
_____________________________________
_____________________________________
15. The number of wolves in the wild in the
northern section of the Coconino county is
decreasing at the rate of 5.0% per year. Your
environmental studies class as counted 80 wolves in
the area.
Part A: Write the function representing the number
of wolves each year.
A. f (t )  80(0.95)t
B. f (t )  80(0.05)t
C. f (t )  80(0.95)t
D. f (t )  80(0.05)t
Answer__________
Part B: After how many years will this population
of 80 wolves drop below 15 wolves, if this rate of
decrease continues?
A. 49 years
B. 3.95 years
C. 34 years
D. 1 year
Answer__________
Algebra 1: Exponentials Unit Review
06/03/14
PUHSD Algebra Curriculum Team