Download Alg 1 Unit 4 Extra Review

1) Simplify the expressions:
Alg 1 Unit 4 Extra Review
a) (y4)6
b) (−3𝑥 3 )2 (2𝑥 2 𝑦 4 )3
2) Simplify the expressions:
a)
4𝑥 −2 𝑦 3
2𝑥 −3 𝑦 −1
8𝑥 3 𝑦
b) 2𝑥 −2 𝑦 4
c)
(4𝑥 2 𝑦 6 )3
(𝑥𝑦 −5 )2
3) Write in radical form.
1
1
a) 3𝑦 2
b) (7𝑥)2
4) Evaluate each of the following:
2
5
a) 2163
b) 7296
5) Solve each of the following:
a) 2x = 256.
b) 3x – 2 = 27
c) 363x – 2 = 216
6) Determine whether the following functions represent exponential growth, exponential decay,
or neither.
a) y = 1.2x4
b) y = 6(1.09)x
c) y = 3(0.92)x
7) Which equation corresponds to the graph shown?
a) y = 3x + 2
c) y = 3(3x)
b) y = 2(3x + 2)
d) y = (2∙3)x + 2
8) Write an equation first for each situation and then solve the problem.
a) A college’s tuition has risen 5% each year since 2000. If the tuition in 2000 was $10,850, write
an equation for the amount of the tuition t years after 2000. Then, predict the cost of tuition
for this college in 15 years.
b) The population of Campbell County, Kentucky, has been decreasing at an average rate of about
0.3% per year. In 2000, its population was 88,647. Write an equation to represent the
population since 2000. If the trend continues, predict the population in 2010.
9) Which statement BEST describes the equation y = A(2.7)x, where A represents the initial value
and x represents time in years?
A) y represents an exponential decay of 2.7%
C) y represents an exponential growth of 2.7%
B) y represents an exponential decay of 170%
D) y represents exponential growth of 170%
10) Write each expression in exponential form.
3
a) ( √𝑥)
8
b) ( √𝑥)
4
3
11) Answer the following questions by comparing and contrasting linear and exponential functions.
a) Kirsten won a contest and can choose the option by which the prize will be awarded to her.
She will be given a payment each day for her lifetime. (assume she is 23 years old and will
live to be 90) The amount, in dollars, she will be paid for each of the first 5 days from
Option 1 and Option 2 are shown in the table.
Day
1
2
3
4
5
Option 1
200
200
200
200
200
Option 2
1
3
9
27
81
Based on this information, which option should she choose so that she can earn the most
money over her lifetime? Explain.
b) The graph below shows an exponential function f(x) and a linear function r(x). Which
statement best explains the behavior of the graphs of the functions as x increases.
A) r(x) eventually exceeds f(x) because rate of change of f(x) increases,
whereas the rate of change of r(x) is constant.
B) r(x) eventually exceeds f(x) because the rate of change of r(x)
increased as x increases, whereas the rate of change of f(x) is constant.
C) f(x) eventually exceeds r(x) because rate of change of r(x) increases,
whereas the rate of change of f(x) is constant.
D) f(x) eventually exceeds r(x) because rate of change of f(x) increases,
whereas the rate of change of r(x) is constant.
11) What is the domain and range for the following functions?:
a) y = 2x
2 𝑥
b) y = (3) − 2
c) y = 4x + 1
Answers:
1a) y 24
1b) 72x12 y12
4 28
2c) 64x y
3a) 3 y
5b) x = 5
5c) x 
7
6
6c) exponential decay
2b)
3b) 7x
5a) x = 8
6a) neither
6b) exponential growth
7) a
8a) y  10850(1  .05)t ;$22,556
t
8b) y  88647(1  .003) ;86,023
9) D
11a) option 2 b/c it’s exponential
11b) D
12a) D: all real #s; R: y >0
12c) D: all real #s; R: y>1
4x 5
y3
2a) 2xy 4
8
10a) x 3
12b) D: all real #s; R: y > -2
3
10b) x 4