CP -Algebra 1
Unit 6 Targets
6.1 Big idea: Simplifying Exponential Expressions and Applying Properties
Target
Example
I can multiply exponential
expressions (including scientific
notation)
I can raise a product to a power
(including scientific notation)
1.
Simplify the following expressions. Evaluate numeric values when possible.
5
3
a. 52 53
b.
d.  4.2 x 103 3.1 x 105  e. 4 5.6  106
335 32  c. x  x
2.
Simplify the following expressions. Evaluate numeric values when possible.
3.
I can divide exponents with the same
base (including scientific notation)
3.
Simplify the following expressions. Evaluate numeric values when possible.
3x 5 4 y 2
1
1.62  103
8a2b4
2  104
a. 6 y 15 b.
c.
d.
e.
6
3
6
5
6y x
y
20ab
8  107
2  10
4.
I can raise a quotient to a power
4.
Simplify the following expressions. Evaluate numeric values when possible.
I can simplify expressions with zero
exponents
5.
 a3 
1  2x 2 
a
a.   b.  5 
c.


4 x 5  y3 
b
 2b 
Simplify the following expressions. Evaluate numeric values when possible.
I can simplify expressions with
negative exponents
6.
I can apply properties of exponents
for integer exponents to fractional
exponents
7.
1.
2.

 
a. b2
7
b.  2xy 
6.
7.
c. x 2u4

4
8
5.

8
a.  9
0
d. 2.1  103

4
5

b. 90

6

c. 8mn3

0
Simplify the following expressions. Evaluate numeric values when possible.
3
1
x 6
a. 103
b. 4
c. x 6 x 3
d. 6 y 3
e. 4x 3 y 2
f.
4 y5
y


Simplify the following expressions. Evaluate numeric values when possible.
1
2
3
2
a. 4  4
 3
b.  x 2 
 
4
3
6
 8 20  4
 1 
c.  x 3 y 3  d.  4 2 




6.2 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, decay,
9.
10.
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.
reflections, rate of change, vertical stretch/shrink (steepness) etc.
9.
Determine whether the following equations represent exponential growth or decay. Justify your answer.
a. y  3x
10.
1
b. y   
2
x
3
c. y  2 
5
x
d. y  6x
Graph the following growth models. Be sure to state the asymptote, the domain and range.
1
a. y   4x b. y  3x  2 c. y  2 3x
2
11.
I can graph exponential decay models
(with vertical stretching/shrinking,
reflections, and vertical shifts) by hand
and with a graphing calculator.
11.
Graph the following decay models. Be sure to state the asymptote, the domain and range.
1
a. y  3 
2
x
x
x
2
b. y     1 c. y    .65
3
6.3 Big idea: Distinguishing between Linear and Exponential Functions
12.
13.
14.
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.
Given a graph, I can determine
whether a function is linear or
exponential and justify.
12.
13.
Identify whether each graph represents a linear or exponential function. Justify your reasoning. Then state the
asymptote, domain and range.
a.
b.
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.
I can determine whether a function is
linear or exponential to complete a
table and write an equation
representing the table.
15.
Identify the common difference/ratio to complete the table and write an equation representing the table.
a.
x
y
0
1
2
5
3
10
4
15
5
b.
x
y
0
1
2
5
3
10
4
20
5
16.
I can write and solve exponential
growth word problems.
16.
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)
I can make predictions using the
curve of best fit (exponential
regression)
I can choose an appropriate
regression to properly model data.
1820.
19.
20.
You deposit $200 in a savings account that earns 3% interest compounded yearly.
a.
Write a function that models the value of the savings account over time.
b.
Find the balance in the account after 5 years
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.
Write a function that models the value of the bus over time.
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 predict the value when x  20 .
e.
Is this an example of interpolation or extrapolation?
12
127
13
140
14
164
15
191
16
214
6.4 Big idea: Writing 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.
1
2
Find the common ratio of the following sequence… 4,2,1, ,...
State whether the following sequences are arithmetic or geometric and then identify the common difference or ratio.
a. 3, 9, 27, 81, 243,…
b. 3, 6, 9, 12, 15,….
c. an  4n  5
d.
23.
I can write the explicit rule for a
geometric sequence
23.
an  3 2n
a. Given a0  5 and r  2 , write an explicit rule for the nth term of the sequence.
1
, write an explicit rule for the nth term of the sequence.
2
c. Identify y-intercept ( a0 ) for the sequence above (part b)
d. Given the sequence 2, 8, 32, 128,… write an explicit rule for the nth term of the sequence.
e. Find a12 for the sequence above (part d)
b. Given a2  1 and r 
Solutions
1a. 55  3125
1b. 38  6561
2d. 1.94481  1013
3a. y 9
5a. 1
3b. 8.1  10
5b. -1
1c. x 8
3c.
7
1
4x 6 y5
9c. decay-explain!
6f.
12. answers will
vary – refer to Day
7 notes for help
16a.
y  200 1  .03
b. $231.85
x
2x 2
y4
5c. 1
1d. 1.302 101
3d.
2a
5b2
3e. 2.5 102
6a.
1
1

3
10 1000
6b. y 4
1
x3
6d.
4c.
8x 5
y 15
6e.
x9
64 y 6
D:
D:
D:
D:
D:
R: y 2
Asy : y  2
14a. exponential
decay – explain
why!
R: y 0
Asy : y  0
14b. linear –
explain why!
R: y 0
Asy : y  0
14c. exponential
growth – explain
why!
R : y  1
Asy : y  1
15a. y  5x  5
R: y 0
Asy : y  0
15b. y 
22a. geometric;
r 3
22c. arithmetic;
d4
23a. an  5 2
D:
R: y 0
Asy : y  0
13b. linear
D:
c. r  0.98
d. 593.87
e. extrapolation
6c.
a12
16b20
11c.
10b.
b. $31,209.37
4b.
11b.
10a.
y  54000 1  .03
a8
b8
11a.
9d. growth
(reflected)explain!
x
4a.
10c.
7c. x 2 y5
R:
Asy : none
18-20.
a. exponential
x
b. y  11.131.22
2c. x12u24
2b. 256x 8 y 8
8. answers will
vary
7b. x 6
R: y 0
Asy : y  0
17a.
2a. b14
6
y3
9a. growthexplain!
7a. 16
13a. exponential
D:
1e. 2.24  107
21. r 
1
2
7d.
1
64
22b. arithmetic;
d 3
22d. geometric;
r 2
9b. decay-explain!
y  1.252
n
1
23b. an  4  
2
23c. a0  4
23d. an 
n
x
1 n
 4
2
23e.
a12  8,388,608