College Algebra Assignment Handout Assignment 8.1: Interpreting Exponential and Logarithmic Functions Complete the following problems. Be sure to show all work. 1) Sketch the graph of each of the following exponential functions. Make sure you label at least three points on the graph or include a t-chart with the coordinates. a. x x f 3 ) ( = b. 3 2 1 + = - x y c. x x g - ÷ ø ö ç è æ = 3 1 ) ( d. 1 4 3 - ÷ ø ö ç è æ = x y e. 1 ) ( + = - x e x f 2) Solve each problem. a. Find the amount accumulated if $10,000 is invested for 5 years at a rate of 5.9% compounded monthly. b. Find the amount accumulated if $50,000 is invested for 20 years at a rate of 7 % compounded daily. c. Find the amount accumulated if $10,000 is invested for 5 years at a rate of 5.9% compounded continuously. 3) Evaluate each expression. a. 81 log 3 b. 9 log 3 1 c. 16 1 log 4 d. 1 log 5 4) Sketch the graph of each of the following logarithmic functions. Make sure you label at least three points on the graph or include a t-chart with the coordinates. a. ) 2 ( log ) ( 2 - - = x x f b. - 4 ) 1 ( log ) ( 3 - + = x x f c. 2 ln ) ( + = x x g 5) Use the properties to expand each logarithmic expression as much as possible. a. ÷ ÷ ø ö ç ç è æ z y x 2 log b. ÷ ÷ ø ö ç ç è æ 2 10 2 log y x c. 3 3 4 2 log z y x 6) Use the properties to condense each logarithmic expression. Your final answer should be a single logarithm with a coefficient of 1. a. ) log (log log z y x + - b. z y x log ) log( 2 1 ) 2 log( + - + c. [ ] y z x log log 2 log 3 1 - + College Algebra Handout Assignment 8.1, V2.4 Page 1 of 2 11/10/2019 © 2012 Pearson Education _1367732981.unknown _1367732986.unknown _1367732988.unknown _1367732990.unknown _1367732991.unknown _1367732992.unknown _1367732989.unknown _1367732987.unknown _1367732983.unknown _1367732984.unknown _1367732982.unknown _1367732977.unknown _1367732979.unknown _1367732980.unknown _1367732978.unknown _1367732975.unknown _1367732976.unknown _1367732974.unknown _1234714280.bin 2 Running head: “FOR PROFIT” CORPORATIONS BE ALLOWED TO RUN U.S. PRISONS? 2 “FOR PROFIT” CORPORATIONS BE ALLOWED TO RUN U.S. PRISONS? SHOULD PRIVATE “FOR PROFIT” CORPORATIONS BE ALLOWED TO RUN U.S. PRISONS? A Review of the Literature Author Note SHOULD PRIVATE “FOR PROFIT” CORPORATIONS BE ALLOWED TO RUN U.S. PRISONS? A Literature review While the private corporations have reportedly been playing an important role in the correctional sector, current researches suggest that permitting ‘for profit' corporations to run the U.S. prisons poses a great threat to human rights as far as the prison inmates are concerned. According to Ahmed (2019), the United States hosts more prisoners than the residents in big American cities like Phoenix. As of 2018, the U.S. Bureau of Justice Statistics estimated the prison inmates to be at 2 million. 128,063 of them were in private correctional facilities, an increase of 4 ...

1. College Algebra
Assignment Handout
Assignment 8.1: Interpreting Exponential and Logarithmic
Functions
Complete the following problems. Be sure to show all work.
1) Sketch the graph of each of the following exponential
functions. Make sure you label at least three points on the graph
or include a t-chart with the coordinates.
a.
x
x
f
3
)
(
=
b.
3
2
1
+
=
-
x
y
c.

2. x
x
g
-
÷
ø
ö
ç
è
æ
=
3
1
)
(
d.
1
4
3
-
÷
ø
ö
ç
è
æ
=
x
y
e.
1
)

3. (
+
=
-
x
e
x
f
2) Solve each problem.
a. Find the amount accumulated if $10,000 is invested for 5
years at a rate of 5.9% compounded monthly.
b. Find the amount accumulated if $50,000 is invested for 20
years at a rate of 7 % compounded daily.
c. Find the amount accumulated if $10,000 is invested for 5
years at a rate of 5.9% compounded continuously.
3) Evaluate each expression.
a.
81
log
3
b.
9
log
3
1
c.
16
1
log
4

4. d.
1
log
5
4) Sketch the graph of each of the following logarithmic
functions. Make sure you label at least three points on the graph
or include a t-chart with the coordinates.
a.
)
2
(
log
)
(
2
-
-
=
x
x
f
b. -
4
)
1
(
log
)
(

5. 3
-
+
=
x
x
f
c.
2
ln
)
(
+
=
x
x
g
5) Use the properties to expand each logarithmic expression as
much as possible.
a.
÷
÷
ø
ö
ç
ç
è
æ
z
y
x
2

6. log
b.
÷
÷
ø
ö
ç
ç
è
æ
2
10
2
log
y
x
c.
3
3
4
2
log
z
y
x
6) Use the properties to condense each logarithmic expression.
Your final answer should be a single logarithm with a
coefficient of 1.
a.

7. )
log
(log
log
z
y
x
+
-
b.
z
y
x
log
)
log(
2
1
)
2
log(
+
-
+
c.
[
]
y
z
x
log
log

8. 2
log
3
1
-
+
College Algebra Handout Assignment 8.1, V2.4
Page 1 of 2
11/10/2019
© 2012 Pearson Education
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_1234714280.bin
2
Running head: “FOR PROFIT” CORPORATIONS BE
ALLOWED TO RUN U.S. PRISONS?

9. 2
“FOR PROFIT” CORPORATIONS BE ALLOWED TO RUN
U.S. PRISONS?
SHOULD PRIVATE “FOR PROFIT” CORPORATIONS BE
ALLOWED TO RUN U.S. PRISONS?
A Review of the Literature
Author Note
SHOULD PRIVATE “FOR PROFIT” CORPORATIONS BE
ALLOWED TO RUN U.S. PRISONS? A Literature review
While the private corporations have reportedly been
playing an important role in the correctional sector, current
researches suggest that permitting ‘for profit' corporations to
run the U.S. prisons poses a great threat to human rights as far
as the prison inmates are concerned. According to Ahmed
(2019), the United States hosts more prisoners than the
residents in big American cities like Phoenix. As of 2018, the
U.S. Bureau of Justice Statistics estimated the prison inmates to
be at 2 million. 128,063 of them were in private correctional
facilities, an increase of 47% from the year 2000.
The Justice Department is mostly concerned about the
safety of private prisons and their inability to save funds. The
goal of this literature review is to find out whether indeed it is a
good idea to allow 'For profit' corporations to run the prisons in

10. the U.S.
The Trump Administration
Ever since the Trump's election, the spending on private
prisons has doubled. In 2017, the GEO Group one of the largest
private prisons received a $110 million contract to build a
detention facility which benefits the Trump's inaugural
committee and his family business. The Trump Administrations
have had policies on immigration being increased.
Consequentially, more immigrants have been detained in private
prisons which translates to more profits for the facilities while
at the same time putting the lives of these detainees in danger.
In 2017, a total of 21 immigrants died while held up in private
facilities. The Trump Administration has contributed to many of
the immigrants be detained. “Funds meant for other agencies
have been also channeled into the enforcement of immigration"
(Ahmed, 2019).
Living conditions of prisoners
Reportedly, many of the private prisons are overcrowded
with inmates. Despite of the huge funding these facilities get,
prisoners are faced with safety and security threats that may
lead to their death. There are several cases of inmates' death
especially for the immigrants who are intersex. Their human
rights are violated, and their health is at risk.
The hidden profits
The American Legislative Exchange Council (ALEC)
currently supports the privatization of prisons. ALEC seeks to
expand the privatization of prisons through the promotion of use
of prisoners to provide labor, increase private prisons use of
goods and services and increase the number of prisoners. ALEC
has successfully "influenced public policies even without public
participation” (Cooper et al., 2016); and helped pass laws that
deal with criminalization. Joy (2018) claims that private prisons
try to save as much and risk the health of the prisoners.
Privatization of prisons
Due to high number of incarcerations, the private
corporations have held some of these prisoners. The prisoners

11. are "exposed to sexual violence, poor sanitation, overcrowding,
inmate-inmate and staff-inmate confrontations" (Gaes, 2019).
These are just a few reasons why these residents through
various organizations are calling out for the abolishment of
private prisons in New York altogether. Simon (2019) indicates
that the CoreCivic and GEO Group have so far been unable to
secure a contract with New York since 2007. The privatization
of the prisons will save minimal cash if not none.
Discussion
From the thorough literature review, it is evident that
allowing the 'For profit' corporations to run the prisons in the
U.S has more harm than good. With the increase in immigration
policies, many more immigrants are faced with the risk of being
detained. The research indicates that the prison inmates are at
risk when it comes to "physical and sexual violence, health
hazards and violation of their human rights" (Ahmed, 2019). It
can be concluded from the various findings that 'for profit'
corporations are in no place supposed to be running prisons in
the U.S.
The major limitation in this literature review is the lack of
evidence on the connection between privatization of prisons in
the U.S and the mass incarceration. Although there has been an
increase of detainees in the Trump Administration's era, their
fate does not depend on the facilities they are detained in. It is
recommended that thorough research be conducted to establish
the various causes of mass incarceration in both private and
public facilities.
Conclusion
As of today, 'For profit' corporations have been and are
currently involved in the American Justice system. While
research has pointed out the need to scrap out private prisons, it
is uncertain if indeed it will be possible. The private prisons are
more concerned by how they can pocket more profit and not the
prisoner's welfare. “The human rights of the prisoners should be
respected and protected" (Joy, 2018). Private prisons get profit
by promoting prison labor and maintaining a certain number of

12. prisoners being held at a given time. Eliminating private
prisons will highly benefit the prisoners. However, more
research is needed to come up with correct data when it comes
to the conditions in the detention facilities, the number of
prisoners and their link with privatization of prisons.
References
Ahmed, H. (2019). How Private Prisons Are Profiting Under the
Trump Administration. Retrieved 25 September 2019, from
https://www.americanprogress.org/issues/democracy/reports/201
9/08/30/473966/private-prisons-profiting-trump-administration/
Cooper, R., Heldman, C., Ackerman, A. R., & Farrar-Meyers,
V. A. (2016). Hidden corporate profits in the US prison system:
the unorthodox policymaking of the American Legislative
Exchange Council. Contemporary Justice Review, 19(3), 380-
400.
Gaes, G. G. (2019). Current status of prison privatization
research on American prisons and jails. Criminology & Public
Policy, 18(2), 269-293
Joy, T. (2018). The Problem with Private Prisons. Retrieved 25
September 2019, from http://www.justicepolicy.org/news/12006
Simon, M. (2019). New York Could Become First State To Be
Completely Done With Private Prisons. Retrieved 11 October
2019, from
https://www.forbes.com/sites/morgansimon/2019/06/18/new-
york-to-become-first-state-to-be-completely-done-with-private-
prisons/.