Algebra 1: Honors Exponentials Unit 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.
Name ______________________________________
Period _______________ Date _________________
4. Using the geometric sequence 3, 5, 9, 17, 33
answer the following:
Part A: Write a function to represent the sequence
above.
1. Make a function table to represent the first five
terms of the sequence 8, 11, 14, 17, 20,…
Part B: Find the 10th term.
5. The population of a sample of bacteria doubles
every 4 minutes.
Using a0 to represent the initial population of the
sample, Sam wrote the equation
to
predict the population at after t minutes.
Answer: ________________
2. Find the 9th term for the sequence a(n)  10  7n
.
Part A: Complete the table of values below and use
it to show that Sam’s equation is incorrect.
Time
Population
0 min
40
4 min
Answer: ________________
3. Find the first five terms of the sequence
a(n)  4n  3
a.
b.
c.
d.
Part B: Write an equation that will accurately
predict the population at after t minutes of a sample
of bacteria that doubles every 4 minutes.
1, 5, 9, 13, 17
1, 2, 3, 4, 5
1, 13, 61, 253, 1021
–2, 1, 13, 61, 253
Answer: ________________
Algebra 1: Exponentials Unit Review
11/22/14
PUHSD Algebra Curriculum Team
II.
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.
6. Part A: Given the function 𝑔(𝑥) = 2 ∙ 3𝑥 graph,
which graph of ℎ(𝑥) shows a shift down 4 units on the
same plane.
a.
b.
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.
Given two functions 𝑓(𝑥) = 5𝑥 and 𝑔(𝑥) = 5𝑥
answer questions 8-10.
8. Using the linear function, evaluate for
x = -2, -1, 0, 1, 2 and show your work. Then prove
that the function grows by a constant rate.
x
g(x)
-2
-1
0
1
2
c.
d.
9. Using the exponential function, evaluate for
x = -2, -1, 0, 1, 2 and show your work. Then prove
that the function has a common ratio.
x
f(x)
Part B: Write the function of ℎ(𝑥)
-2
-1
0
1
2
10. Graph the two functions on the same grid, label
them, and label the coordinates of at least three
point on each graph. Be sure to choose units for
the axes that allow you to show both functions.
7. Use a graphing calculator to determine how the
graph of y  5x would be affected if it was
changed to y  5x  2 ?
Select all that apply








Increasing to decreasing
Decreasing to increasing
Shift up 5 units
Shift down 5 units
Shift left 5 units
Shift right 5 units
x-intercept
y-intercept
Algebra 1: Exponentials Unit Review
11/22/14
PUHSD Algebra Curriculum Team
11. Using the graphs shown below, label which
functions are linear and exponential.
What is the correct pair of values? Explain how you
found your answers.
Answer:
__________________________________________
__________________________________________
__________________________________________
__________________________________________
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.
13. Write an equation for the function and label as
exponential growth or exponential decay.
12. Mary received a gift card to her favorite yogurt
shop. Each yogurt at the shop costs the same
amount, so the relationship between the amount of
money left on her card v and the total number of
yogurts she has purchased s can be represented by a
linear function. After several weeks of purchasing
yogurt, Mary went online to see the amount of
money left on her card. She noticed that one row in
the table below did not make sense.
14.What is the rule for the table below?
Original Value of Card: $25.00
Total Smoothies Purchased
Value of Card (v)
with Card (s)
2
21.00
4
17.00
6
13.50
8
9.00
10
5.00
x
y
-2
2
-1
4
0
8
1
16
2
32
Which pair of values in the table is incorrect?
Answer:__________
Answer:
__________________________________________
__________________________________________
Algebra 1: Exponentials Unit Review
11/22/14
PUHSD Algebra Curriculum Team
15. Maria won $1000 in a mathematics competition.
She invests the money in an interest-earning account.
The table shows how much money she has in the
account.
17. Part A: Complete the table below.
x
0
2
4
6
8
10
Maria’s Account
Year
0
1
2
3
4
Value o
$1000.00
$1050.00
$1102.50
$1157.63
$1215.51
𝒇(𝒙) = 𝟐𝒙
𝒈(𝒙) = 𝟑𝒙
𝒉(𝒙) = 𝟐𝒙𝟐
Part A: Write an appropriate model for the amount
that Maria will have in the account after t years.
Part B: List the functions in decreasing order of
which function increases fastest as x gets larger and
larger.
Part B: Use the model you chose to predict
approximately when Maria will have $1500 in the
account.
Part C: Can you determine this order in any way
other than a table? Explain.
V. F-LE.3 Learning Target: I can compare
exponential growth to linear growth using graphs
and tables.
VI.
16. Use the graph below to answer the following
parts.
F-LE.5 Learning Target: I can identify
common ratio (b) and initial value (a) of
y  ab x from a given context.
18. Based on the change per unit interval, choose
an appropriate type of function to model the
situation. Justify your response.
Population Decay of Bacteria
Time (hours)
Number of
Bacteria
0
90,000
1
27,000
2
8,100
3
2,430
4
729
a. Linear
b.Exponential
Part A: For the interval 0 ≤ 𝑥 ≤ 49 which function
appears to increase the fastest?
Answer:__________
Justification: _________________________
Part B: For the interval 𝑥 ≥ 49 which functions
appears to increase the fastest?
_____________________________________
_____________________________________
Algebra 1: Exponentials Unit Review
11/22/14
PUHSD Algebra Curriculum Team
19. Consider the graph of function 𝑓(𝑥) = 1.5(2)𝑥
What type of function is 𝑓(𝑥)? Explain how you
know.
Part B: After how many years will this population
of 80 wolves drop below 15 wolves, if this rate of
decrease continues?
20. A small company had an average monthly
electricity use of 8000 kilowatt-hours last year.
Their five-year plan calls for their monthly
electricity use to be reduced by 10% each of the
next five years. Identify the following.
Initial Value: ____________________
Common Ratio: __________________
Equation: _______________________
21.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
b.
f (t )  10000(1.11)t
c.
f (t )  10000(12)t
d.
f (t )  10000(0.11)t
22. 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 has 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__________
Algebra 1: Exponentials Unit Review
11/22/14
PUHSD Algebra Curriculum Team