CP -Algebra 1
Unit 6 Student Targets
Name:_________________________________________
Teacher:___________________Pd:_____Date:____
Big idea: Simplifying and Applying Exponential Expressions
Target
Example
I can multiply exponential
expressions (including scientific
notation)
I can raise a product to a power
(including scientific notation)
I can divide exponents with the same
base (including scientific notation)
1.
4.
I can raise a quotient to a power
4.
5.
I can evaluate expressions with zero
or negative exponents
5.
6.
I can simplify expressions with zero
or negative exponents
6.
1.
2.
3.
2.
3.
Multiply the following expressions…
a. 52 53
b.
35  3 c. x 5  x 3
 
Simplify… a. b2
7
a.  2  3
d. (4.2 x 103 )(3.1 x 105 )
b.  x  y 
3

8
1 15
x 5 y2
1.62  103
y b.
c. 6 3
6
5
y x
y
2  10
Simplify… a.
a
Simplify… a.  
b
8
 a3 
b.  5 
 2b 
4
b.  
3
3
Evaluate… a. 10
4
6
d.

d. 2.1  103


4
a2b4
ab6
5
c.
1  2x 2 


4 x 5  y3 
0
c. 4 6 43
1
54
d.

b. a2b4
Simplify… a. 6 y 4

c. x 2  u4

e. 4 5.6  106
c. 4x 3 y 2

3

d. 8mn3

0
e.
x 6
4 y5
Big idea: Using Fractional Exponents
7.
I can apply properties of exponents
for integer exponents to fractional
exponents
7.
1
2
3
2
Evaluate… a. 4  4
 3
b.  22 
 
4
3
 8 20  4
c.  x 3 y 3  d.


6
 21 
4 


Big idea: Writing and Graphing Exponential Growth and Decay Functions
8.
I can identify the characteristics of
8.
Given the function y  abx  c , explain how ‘a’, ‘b’, and ‘c’ each affect the graph of the function. (Include growth,
9.
10.
11.
exponential growth and decay
functions.
I can identify when an exponential
function models growth or decay.
I can graph exponential growth
models (with vertical
stretching/shrinking, reflections, and
vertical shifts) by hand and with a
graphing calculator.
I can graph exponential decay models
(with vertical stretching/shrinking,
reflections, and vertical shifts) by
hand and with a graphing calculator.
decay, reflections, rate of change, etc).
9.
Determine whether the following equations represent exponential growth or decay. Justify your answer.
10.
1
3
a. y  3
b. y 
c. y  2   d. y  6x
2
5
Graph the following growth models:
1
a. y  3  2x b. y   4x c. y  3x  2 d. y  2 3x
2
11.
Graph the following decay models:
x
x
x
1
a. y  3   
2
x
b.
1 1
y   
2 3
x
x
x
2
c. y     1 d. y    .65
3
Big idea: Distinguishing between Linear and Exponential Functions
12.
Compare and contrast the characteristics (general shape, rate of change, asymptotes, domain and range) of y  3x
I can compare and contrast the
characteristics of linear and
exponential functions.
12.
13.
Given a graph, I can determine
whether a function is linear or
exponential and justify.
13.
Identify whether each graph represents a linear or exponential function. Justify your reasoning.
a.
b.
14.
Given a table of values, I can
determine whether a function is
linear or exponential and justify.
14.
Tell whether the table of values represents a linear function or an exponential (growth or decay) function. Justify your
reasoning.
a.
X
-2
-1
0
1
2
Y
-8
-4
-2
-1
-0.5
and y  3x .
b.
X
Y
-4
-7
-2
-4
0
-1
2
2
4
5
X
Y
0
1
1
1.5
2
2.25
3
3.375
4
5.0625
c.
15.
16.
I can determine whether a function is
linear or exponential to complete a
table.
I can write and solve exponential
growth word problems.
15.
16.
Complete the table based on the given information.
a.
X
Y
0
1
2
5
3
10
4
15
5
b.
X
Y
0
1
2
5
3
10
4
20
5
You deposit $200 in a savings account that earns 3% interest compounded yearly.
a.
Use the information to write an exponential growth model
b.
Find the balance in the account after 5 years
17.
I can write and solve exponential
decay word problems
17.
18.
I can use the graphing calculator to write
an equation for the curve of best fit
(exponential regression)
1820.
19.
I can make predictions using the curve of
best fit (exponential regression)
20.
I can choose an appropriate regression to
properly model data.
A school district bought a bus in 1990 for $54,000. The value of the bus has been decreasing at a rate of 3% per year.
a.
Use the information to write an exponential decay model
b.
What was the approximate value of the bus in 2008?
Use the table below to answer the following questions:
X 0
1
2
3
4
5
6
7
8
9
10 11
Y 8
11 15 20 27 35 44 56 69 83 99 114
a.
Does the data most closely model a linear or exponential function?
b.
Write the equation of the line/curve of best fit.
c.
What is the correlation coefficient?
d.
Use your model to estimate the value when x is 20.
e.
Is this an example of interpolation or extrapolation?
12
127
Big idea: Writing and Graphing Geometric Sequences
21.
I can find the common ratio of a
geometric sequence
21.
22.
I can differentiate between arithmetic
and geometric sequences and justify.
22.
23.
I can graph a geometric sequence
23.
State whether the following sequence is arithmetic or geometric. Find the next 2 terms.
a. 3, 9, 27, 81, 243,…
b. 3, 6, 9, 12, 15,….
Graph the following geometric sequence… 2, 4, 8, 16, 32,…
24.
I can write the general rule for a
geometric sequence.
24.
Write a general rule for the nth term of the sequence 2, 8, 32, 128,… . Then find a12
1
2
Find the common ratio of the following sequence… 4,2,1, ,...
13
140
14
164
15
191
16
214
Solutions
1a. 55  3125
2d. x12u24
4c.
8x 5
y 15
1b. 36  729
2e. 1.94481 x 1013
5a.
1
1

3
10 1000
1c. x8
1d. 1.302 x 10-1
3a. y9
3b. 8.1 x 107
5b. 1
5c.
1
1

3
4 64
1e. 2.24 x 107
3c.
x2
y4
5d. 54  625
2a. b14
3d.
6a.
2b. 63  216
a
b2
4a.
6
y4
a8
b8
a2
b4
9a. growth-explain!
6b.
4b.
a12
16b20
6c.
x9
64 y 6
6d. 1
7a. 42  16
7b. 26  64
7c. x 2 y5
9c. decayexplain!
9d. growth
(reflected)-explain!
10a.
10b.
10c.
10d.
11a.
11b.
11c.
11d.
12. answers
will vary.
13a. exponential—
explain!
13b. linear—
explain!
14a. exponential
decay—explain!
14b. linear—
explain!
14c. exponential
growth—explain!
15a. -5, 0, 20
15b. 1.25, 2.5, 40
16a. 14.
t
y  2001  .03
17a.
t
y  54000 1  .03
18a.
exponential
18b.
18c. r  .98
18d. 593.87
16b. $231.85
22a. geometric
729, 2187
17b. $31,209.37
22b. arithmetic
18, 21
23.
18e.
extrapolation
21. r 
1
2
7d.
1
64
8. answers will
vary
2c. x8y8
y  11.131.22
1 n
4
2
a12  8,388,608
24. an 
x
9b. decay-explain!