1. Exponential expressions, equations, inequalities, and functions involve expressions of the form abx-c + d, where b > 0 and b ≠ 1. 2. An exponential equation sets two exponential expressions equal to each other, while an exponential inequality compares two exponential expressions. 3. An exponential function expresses a relationship between two variables, usually of the form f(x) = bx, where b > 0 and b ≠ 1.

1. General
Mathematics
Quarter 1 – Module 5:
Exponential Functions
11

2. General Mathematics – Grade 11
Self-Learning Module (SLM)
Quarter 1 – Module 5: Exponential Functions
First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of
the Government of the Philippines. However, prior approval of the government agency or office
wherein the work is created shall be necessary for exploitation of such work for profit. Such
agency or office may, among other things, impose as a condition the payment of royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names,
trademarks, etc.) included in this module are owned by their respective copyright holders.
Every effort has been exerted to locate and seek permission to use these materials from their
respective copyright owners. The publisher and authors do not represent nor claim ownership
over them.
Printed in the Philippines by Department of Education – SOCCSKSARGEN Region
Office Address: Regional Center, Brgy. Carpenter Hill, City of Koronadal
Telefax: (083) 2288825/ (083) 2281893
E-mail Address: region12@deped.gov.ph
Development Team of the Module
Writers: Nathaniel A. Galopo, Erwin G. Aragon,
Charmaine Joy C. Barago, Mariel G. Villanueva
Editors: Venus P. Enumerables, Ian Caesar E. Frondoza
Reviewers: Venus P. Enumerables, Ian Caesar E. Frondoza
Illustrator:
Layout Artist: Maylene F. Grigana
Cover Art Designer: Ian Caesar E. Frondoza
Management Team: Allan G. Farnazo, CESO IV – Regional Director
Fiel Y. Almendra, CESO V – Assistant Regional Director
Gildo G. Mosqueda, CEO V
Diosdado F. Ablanido, CPA
Gilbert B. Barrera – Chief, CLMD
Arturo D. Tingson Jr. – REPS, LRMS
Peter Van C. Ang-ug – REPS, ADM
Jade T. Palomar – REPS, Mathematics
Donna S. Panes – Chief, CID
Elizabeth G. Torres – EPS, LRMS
Judith B. Alba – EPS, ADM
Reynaldo C. Tagala – EPS, Mathematics

3. 11
General
Mathematics
Quarter 1 – Module 1:
Representing Real – Life Situations
Using Exponential Functions

4. 2
Introductory Message
For the facilitator:
Welcome to the Grade 11 General Mathematics Self-Learning Module (SLM) on
Representing Real – Life Situations Using Exponential Functions!
This module was collaboratively designed, developed and reviewed by educators both
from public and private institutions to assist you, the teacher or facilitator in helping
the learners meet the standards set by the K to 12 Curriculum while overcoming
their personal, social, and economic constraints in schooling.
This learning resource hopes to engage the learners into guided and independent
learning activities at their own pace and time. Furthermore, this also aims to help
learners acquire the needed 21st century skills while taking into consideration their
needs and circumstances.
In addition to the material in the main text, you will also see this box in the body of
the module:
As a facilitator you are expected to orient the learners on how to use this module.
You also need to keep track of the learners' progress while allowing them to manage
their own learning. Furthermore, you are expected to encourage and assist the
learners as they do the tasks included in the module.
Notes to the Teacher
This contains helpful tips or strategies that
will help you in guiding the learners.

5. 3
For the learner:
Welcome to the Grade 11 General Mathematics Self-Learning Module (SLM) on
Representing Real – Life Situations Using Exponential Functions!
The hand is one of the most symbolized part of the human body. It is often used to
depict skill, action and purpose. Through our hands we may learn, create and
accomplish. Hence, the hand in this learning resource signifies that you as a learner
is capable and empowered to successfully achieve the relevant competencies and
skills at your own pace and time. Your academic success lies in your own hands!
This module was designed to provide you with fun and meaningful opportunities for
guided and independent learning at your own pace and time. You will be enabled to
process the contents of the learning resource while being an active learner.
This module has the following parts and corresponding icons:
What I Need to Know This will give you an idea of the skills or
competencies you are expected to learn in the
module.
What I Know This part includes an activity that aims to check
what you already know about the lesson to take.
If you get all the answers correct (100%), you may
decide to skip this module.
What’s In This is a brief drill or review to help you link the
current lesson with the previous one.
What’s New In this portion, the new lesson will be introduced
to you in various ways such as a story, a song, a
poem, a problem opener, an activity or a situation.
What is It This section provides a brief discussion of the
lesson. This aims to help you discover and
understand new concepts and skills.
What’s More This comprises activities for independent practice
to solidify your understanding and skills of the
topic. You may check the answers to the exercises
using the Answer Key at the end of the module.
What I Have Learned This includes questions or blank
sentence/paragraph to be filled in to process what
you learned from the lesson.
What I Can Do This section provides an activity which will help
you transfer your new knowledge or skill into real
life situations or concerns.
Assessment This is a task which aims to evaluate your level of
mastery in achieving the learning competency.
Additional Activities In this portion, another activity will be given to
you to enrich your knowledge or skill of the lesson
learned. This also tends retention of learned
concepts.

6. 4
Answer Key This contains answers to all activities in the
module.
At the end of this module you will also find:
The following are some reminders in using this module:
1. Use the module with care. Do not put unnecessary mark/s on any part of the
module. Use a separate sheet of paper in answering the exercises.
2. Don’t forget to answer What I Know before moving on to the other activities
included in the module.
3. Read the instruction carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking your answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are through with it.
If you encounter any difficulty in answering the tasks in this module, do not
hesitate to consult your teacher or facilitator. Always bear in mind that you are
not alone.
We hope that through this material, you will experience meaningful learning and
gain deep understanding of the relevant competencies. You can do it!
References This is a list of all sources used in developing this
module.

7. 5
What I Need to Know
This module was designed and written with you in mind. It is here to help you master
representing real – life situations using exponential functions. The scope of this
module permits it to be used in many different learning situations. The language
used recognizes the diverse vocabulary level of students. The lessons are arranged
to follow the standard sequence of the course. But the order in which you read them
can be changed to correspond with the textbook you are now using.
This module presents the lessons in the following outline:
1. Definition of Exponential Expression
2. Description and examples of Exponential Function, Exponential Equation
and Exponential Inequalities
3. Exponential functions and their transformations
4. Exponential growth and decay
5. Compound interest
6. The natural exponential function
After going through this module, you are expected to:
1. Define exponential function, exponential equation and exponential
inequalities.
2. Distinguish among exponential function, exponential equation and
exponential inequalities.
3. Know the concept of exponential functions,
4. Differentiate exponential growth and decay, and
5. Represent real - life situations using exponential functions.

8. 6
Write on the answer sheet provided the letter of the correct answer.
For items 1 to 4, determine whether the given expression is an exponential function,
exponential equation, exponential inequality or none of these. Refer to the choices
below.
A. Exponential Function
B. Exponential Equation
C. Exponential Inequality
D. None of these
1. 𝑦 = 3𝑥
2. 4𝑥+1 >
1
64
3. 25𝑥−9
= 4𝑥
4. 5 = 𝑥2
− 6𝑥
5. If a certain growth of bacteria depends upon the formula 𝑦 = 200(4𝑥), what is 𝑦
when 𝑥 = −2?
A. 23.5
B. 22.5
C. 12.5
D. 11.5
6. What is 𝑓(𝑥) = 2−𝑥
if 𝑥 = −3 ?
A. 8
B. 6
C.
1
6
D.
1
8
7. A barangay has 1,000 individuals and its population doubles every 60 years.
What is the barangay’s population in 10 years?
A. 1,008
B. 1,020
C. 1,122
D. 1,182
8. The half-life of a substance is 400 years. What is the exponential model for
this situation if the initial amount is 200 mg?
A. 𝑦 = 200 (
1
2
)
400
𝑡
B. 𝑦 = 200 (
1
2
)
𝑡
400
C. 𝑦 = 400 (
1
2
)
𝑡
400
D. 𝑦 = 400 (
1
2
)
400
𝑡
What I Know

9. 7
9. Php 10,000 is invested at 2% compounded annually. What is the exponential
model for this situation?
A. 𝑦 = 10,000(2)𝑡
B. 𝑦 = 10,000(1.02)𝑡
C. 𝑦 = 10,000(0.2)𝑡
D. 𝑦 = 10,000(0.02)𝑡
10.Which of the situations can be modeled by an exponential function?
A. A radioactive substance decays after t units of time.
B. An amount deposited by Nheytan in Landbank of the Philippines
earns a compounded interest of 7.5% yearly.
C. A certain culture of bacteria doubles every an hour.
D. All of the above
11.What is if ?
A. 25
B. 10
C.
1
5
D.
1
25
12.Myries invested P50,000 after graduation. If the average interest rate is 4.8%
compounded annually, what is the exponential model for the situation?
A. 𝐴 = 50,000(0.048)𝑡
B. 𝐴 = 50,000(1.048)𝑡
C. 𝐴 = 50,000(0.048)𝑡
D. 𝐴 = 50,000(1.048)𝑡
13.The half-life of a substance is 400 years. How much will remain after 600
years if the initial amount was 200 grams?
A. 70.71 grams
B. 68.49 grams
C. 63.97 grams
D. 59.07 grams
14.A certain culture of bacteria grows in number according to the function
(in thousands). After one hour how many bacteria are there?
A. 2
B. 7
C. 10
D. 25
15.The population of the Philippines can be approximated by the function
where x is the number of years since 1955
(e.g. at 1955). Use this model to approximate the Philippine population
during the 1985. Round off answer to the nearest thousand. (Hint: use a
scientific calculator).
A. 42,467,211
B. 44,762,121
C. 46,117,422
D. 47,211,426
x
x
f 5
)
( = 2
−
=
x
t
N 5
2
=
x
.
e
P(x) 0251
0
000
,
000
,
20
= )
40
0
( 
 x
0
=
x

10. 8
Lesson
1
Representing Real-Life Situations
Using Exponential Functions
Exponential functions occur in various real-world situations. Exponential
functions are used to model real-life situations such as population growth,
radioactive decay, carbon dating, growth of an epidemic, loan interest rates, and
investments.
Some things can be counted by multiplying continually. Recall the concept
of geometric sequence (or progression) studied in Grade 10 in which each term
after the first is obtained by multiplying the preceding term by a non-zero constant
called the common ratio.
Symbolically, if is the first term and is the common ratio, then
forms a geometric sequence.
For example, bacteria reproduce by splitting, doubling the number of
bacterial cells. If there are 7 cells and a doctor is examining the bacteria, after a
certain time, there will be 14 cells…then 28… then 56, etc. The terms 7, 14, 28,
56, … can be written in factored form or exponential form as shown in the table
below:
Term In Factored Form In Exponential Form
This means that if there are bacteria initially and doubles after a certain
time, then there will be after units of time.
In general, given the first term and the common ratio is of a geometric
sequence, then the term of the sequence is .
a r
,...
,
,
, 3
2
ar
ar
ar
a
7
1 =
a 7 0
2
7
14
2 =
a 2
7 1
2
7
28
3 =
a 2
2
7 
 2
2
7
56
4 =
a 2
2
2
7 

 3
2
7
  
7
( ) 1
2
7
−
n
n
1
a r
th
n 1
1
−
= n
n r
a
a
What’s In

11. 9
To help you understand exponential functions, do the following activity.
Materials: One 2-meter of string, a pair of scissors
(a) At step 0, there is 1 string.
(b) At step 1, fold the string into two equal parts and then cut at the middle.
How many strings of equal length do you have? Enter your answer in the
table below.
(c) At step 2, again fold each of the strings equally and then cut. How many
strings of equal length do you have? Enter your answer in the table
below.
(d) Continue the process until the table is completely filled-up.
Step
Number of Strings
Questions:
(a) What pattern can be observed from the data?
(b) Define a formula for the number of strings as a function of the step
number.
Answers:
Step
Number of Strings
It can be observed that as the step number increases by 1, the number of
strings doubles. If is the number of strings and is the step number, then
.
0 1 2 3 4 5 6 7
1 2 4 8 16 32 64 128
n s s
s
n 2
)
( =
What’s New
Notes to the Teacher
Folding a paper and determine the relationship between the number
of folds and the number of regions or areas formed is another good
activity that illustrates exponential function.

12. 10
What is It
Definition: An exponential expression is an expression of the form 𝒂 ∙ 𝒃𝒙−𝒄
+ 𝒅
,where (𝒃 > 𝟎, 𝒃 ≠ 𝟏).
The definitions of exponential equations, inequalities and functions are shown below.
Exponential
Equation
Exponential
Inequality
Exponential Function
Definition An equation involving
exponential
expressions
An inequality
involving exponential
expressions
Function of the form
𝑓(𝑥) = 𝑏𝑥 (𝒃 > 0, 𝑏 ≠ 1).
Example
72𝑥−𝑥2
=
1
343
52𝑥 − 5𝑥+1 ≤ 0 𝑓(𝑥) = (1 ⋅ 8)𝑥
or
𝑦 = (1 ⋅ 8)𝑥
An exponential equation or inequality can be solved for all 𝑥 values that satisfy
the equation or inequality. An exponential function expresses a relationship between
two variables (such as 𝑥and 𝑦), and can be represented by a table of values or a
graph.
Solved Examples
Determine whether the given is an exponential function, an exponential equation,
an exponential inequality, or none of these.
1. 𝑓(𝑥) = 5𝑥2
(Answer: None of these)
2. 2 ≥ (
1
2
)
𝑥
(Answer: Exponential Inequality)
3. 74𝑥
= 𝑦 (Answer: Exponential Function)
4. 4(100𝑥−2) = 500 (Answer: Exponential Equation)
5. 7 < 49𝑥+3
(Answer: Exponential Inequality)
6. 𝑦 = 0.5𝑥
(Answer: Exponential Function)

13. 11
Definition
An exponential function with the base is a function of the form or
where , .
The base 𝑏 is restricted to positive real numbers to ensure that is always
a real number. Also, base 𝑏 cannot be equal to 1, for if 𝑏 = 1 , then 𝑓(𝑥) = 1, and it
will be a constant function.
Example 1. Complete a table of values for and for the
exponential functions , , and .
Solution:
Example 2. If , evaluate and .
Solution:
Since is irrational, the rules for rational exponents are not
applicable. We define using rational numbers: can be approximated by
. A better approximation is . Intuitively, one can obtain any level of
accuracy for by considering sufficiently more decimal places of .
Mathematically, it can be proved that these approximations approach a unique
value, which we define to be .
b x
b
x
f =
)
(
x
b
y = 0

b 1

b
)
(x
f
2
1,
0,
,
1
,
2
,
3 −
−
−
=
x 3
x
y 





=
3
1 x
y 10
= ( )x
y 8
.
0
=
x 3
− 2
− 1
− 0 1 2 3
x
y 





=
3
1
27 9 3 1
3
1
9
1
27
1
x
y 10
=
1000
1
100
1
10
1
1 10 100 1000
( )x
y 8
.
0
= 1.953125 5625
.
1 25
.
1 1 8
.
0 64
.
0 512
.
0
x
x
f 3
)
( = ( )
4
.
0
,
2
1
),
2
(
),
2
( f
f
f
f 





− )
(
f
9
3
)
2
( 2
=
=
f
9
1
3
1
3
)
2
( 2
2
=
=
=
− −
f
3
3
2
1 2
1
=
=






f
( ) 5
5 2
5
2
4
.
0
9
3
3
3
4
.
0 =
=
=
=
f
14159
.
3



3 ( ) 
 3
=
f
14
.
3
3 14159
.
3
3

3 

3

14. 12
Definition
Let be a positive number not equal to 1. A transformation of an exponential
function with base b is a function of the form
.
where , and are real numbers.
There are many real-life situations that can be represented using exponential
functions and their transformations. Some of them are population growth,
exponential decay, and compound interest.
Population Growth
On several instances, scientists will start with a certain number of bacteria or
animals and watch how the population grows. For example, if the population doubles
every 3 days, then this can be represented as an exponential function.
Example 3. Let . At , there were initially 20 bacteria. Suppose
that the bacteria double every 100 hours. Give an exponential model for the
bacteria as a function of .
Solution:
Initially,
An exponential model for this situation is .
Exponential Model for Population Growth
Suppose a quantity doubles every units of time. If is the initial amount,
then the quantity after units of time is given by
.
b
d
b
a
x
f c
x
+

= −
)
(
a c d
hours
in
time
=
t 0
=
t
t
20
bacteria
of
Number
,
0
At =
=
t
2
20
bacteria
of
Number
,
00
1
At 
=
=
t
2
2
20
bacteria
of
Number
,
00
2
At 
=
=
t
3
2
20
bacteria
of
Number
,
00
4
At 
=
=
t
( )100
2
20
t
y =
y T 0
y
y t
( ) T
t
y
y
/
0 2
=

15. 13
Radioactive Decay
The disintegration of substances is another situation that shows exponential
change. Each hour, a fraction of the atoms of a radioactive substance randomly
changes into different atoms, i.e. they decay.
Definition
The half-life of a substance is the time it takes for half of the substance to decay.
.
Example 4. Suppose that the half-life of a certain radioactive substance is 10 days
and there are 10 g initially. (a) Determine the amount of substance remaining after
30 days, and (b) give an exponential model for the amount of remaining substance.
Solution: We use the fact that the mass is halved every 10 days (from the definition
of half-life). Let . Thus, we have
Initially,
(a) The amount of substance remaining after 30 days is .
(b) An exponential model for this situation is .
Exponential Model for Radioactive Decay
If the half-life of a substance is units, and is the amount of the substance
corresponding to , then the amount of substance remaining after units of
time is given by
days
in
time
=
t
g
t 10
substance
of
Amount
,
0
At =
=
g
t 5
2
1
0
1
substance
of
Amount
,
10
At =






=
=
g
t 5
.
2
2
1
0
1
substance
of
Amount
,
20
At
2
=






=
=
g
t 25
.
1
2
1
0
1
substance
of
Amount
,
30
At
3
=






=
=
g
25
.
1
10
2
1
0
1
t
y 





=
T 0
y
0
=
t y t
T
t
y
y 





=
2
1
0

16. 14
Compounded Interest
A starting amount of money (called the principal) can be invested at a certain
interest rate that is earned at the end of a given period of time (such as one year). If
the interest rate is compounded, the interest earned at the end of the period is added
to the principal, and this new amount will earn interest in the next period. The same
process is repeated for each succeeding period: interest previously earned will also
earn interest in the next period.
Example 5. Mrs. Dela Cruz invested Php 100,000.00 in a company that offers 6%
interest compounded annually. Define an exponential model for this situation. How
much will this investment be worth at the end of each year for the next five years?
Solution: Let be the time in years. Then we have:
Initially,
Following the pattern, we can simply solve a certain amount of
investment at period of time.
An exponential model for this situation is or simply
.
t
00,000
1
investment
of
Amount
,
0
At =
=
t
( )
106,000
Php
06
.
0
1
100,000
06)
100,000(0.
00,000
1
investment
of
Amount
,
1
At
=
+
=
+
=
=
t
( ) ( )( )
( )( )
( )
12,360
1
Php
06
.
0
1
100,000
06
.
0
1
06
.
0
1
100,000
06
.
0
06
.
0
1
100,000
06
.
0
1
100,000
0.06)
1
(
00,000
1
investment
of
Amount
,
2
At
2
=
+
=
+
+
=
+
+
+
=
+
=
=
t
( ) ( ) ( )
( ) ( )
( )
19,101.60
1
Php
06
.
0
1
100,000
06
.
0
1
06
.
0
1
100,000
06
.
0
06
.
0
1
100,000
06
.
0
1
100,000
0.06)
1
(
00,000
1
investment
of
Amount
,
3
At
3
2
2
2
2
=
+
=
+
+
=
+
+
+
=
+
=
=
t
t
126,247.70
Php
0.06)
1
(
00,000
1
investment
of
Amount
,
4
At 4

+
=
=
t
133,822.56
Php
0.06)
1
(
00,000
1
investment
of
Amount
,
5
At 5

+
=
=
t
( )t
A 06
.
0
1
000
,
100 +
=
( )t
A 06
.
1
000
,
100
=

17. 15
Exponential Model for Compounded Interest
If a principal is invested at an annual rate of , compounded annually, then the
amount after years is given by
.
Example 6. Referring to Example 5, is it possible for Mrs. Dela Cruz to double her
money in 8 years? 10 years?
Solution: Using the exponential model , we substitute and
:
If , .
If ,
Since Mrs. Dela Cruz money still has NOT reached after 10 years, then
she has not doubled her money during this time.
The Natural Exponential Function
Some situations can be modeled using the exponential function with base ,
an irrational number whose value is approximately 2.71828. At this point, we will
just rely on the scientific calculator to obtain further decimal expansion of .
Definition
The natural exponential function is a function defined by
for all real numbers.
Example 7. A radioactive substance is decaying according to the function
, where milligram is the amount present in years from now. How
much will be left after 10 years?
Solution: Substitute to the given function. Using a scientific calculator, we
have .
P r
t
( )t
r
P
A +
= 1
( )t
A 06
.
1
000
,
100
= 8
=
t
10
=
t
8
=
t ( ) 159,384.81
Php
06
.
1
000
,
100
8

=
A
10
=
t ( ) 179,084.77
Php
06
.
1
000
,
100
10

=
A
200,000
Php
e
e
x
e
x
f =
)
(
x
t
e
y 02
.
0
500 −
= y t
10
=
t
409
500 2
.
0

= −
e
y

18. 16
What’s More
Activity 1 Exponential Function Defined
Determine whether the given is an exponential function, an exponential equation,
an exponential inequality, or none of these.
1. 49𝑥
= 72
2. 3 < 9𝑥
3. 𝑦 = 81𝑥
4. 3(15𝑥) = 45
5. 3 ≥ 9𝑥−1
6. 𝑦 = 1.25𝑥
Activity 2 Evaluation of Exponential Function
Given the exponential functions, complete the table of values for
Activity 3 Exponential Models
Give the exponential model for the following situations:
1. At time , 500 bacteria are in a petri dish, and this amount triples every
15 days.
2. The half-life of a substance is 400 years. Initially, there are 100 g of
substance.
3. Suppose that a couple invested Php 50,000 in an account when their child
was born, to prepare for the child’s college education. The average interest
rate is 4.4 % compounded annually.
2
,
1
,
0
,
1
,
2 −
−
=
x
x 2
− 1
− 0 1 2
x
y 1
.
0
=
x
y 3
=
x
y 





=
5
2
0
=
t

19. 17
What I Have Learned
Choose the term(s), phrases or expressions inside the box to complete the
following sentences.
1. An exponential function with the base is a function of the form ___________
where , .
2. Let be a positive number not equal to 1. A __________of an exponential
function with base b is a function of the form .
3. Common situations that lead to exponential relationships are
___________________-, _______________-, and _________________.
4. The exponential model of a quantity which doubles every units of time
given initial amount and units of time passed is _________.
5. A radioactive substance decays or undergoes a change in its elements after a
period of time. ______________ is the time until only half of the original amount
remains unchanged. It is modeled by the equation __________________ where
the is the amount of substance remaining after units of time, units
of time is the half-life of the substance, and is the amount of the substance
corresponding to .
6. If an amount P is invested at an interest rate r compounded annually, then
the investment will increase to a value A, at the end of t years. It is modeled
by the equation __________________.
7. An exponential function having defined by base e (an irrational number) is
called the _________________ . It is of the form ________ for all real number x.
b
0

b 1

b
b
d
b
a
x
f c
x
+

= −
)
(
y T
0
y t
y t T
0
y
0
=
t
decay of radioactive substances Transformation
compound interest offered by banks Half-life
natural exponential function population growth
( ) T
t
y
y
/
0 2
= x
b
x
f =
)
( x
b
y =
T
t
y
y 





=
2
1
0 ( )t
r
P
A +
= 1 x
e
x
f =
)
(

20. 18
What I Can Do
Activity 4
Use your learning on exponential functions to answer the following:
1. You take out Php 20,000 loan at a 5% interest rate compounded annually.
How much will you owe after 10 years?
2. The population (in millions) of a certain country follows the exponential
growth model , t years after 1994. Predict the population in
the year 2020.
Assessment
Write on the answer sheet provided the letter of the correct answer.
For items 1 to 4, determine whether the given expression is an exponential function,
exponential equation, exponential inequality or none of these. Refer to the choices
below.
A. Exponential Function
B. Exponential Equation
C. Exponential Inequality
D. None of these
1. 𝑦 = 3𝑥
2. 4𝑥+1
>
1
64
3. 25𝑥−9
= 4𝑥
4. 5 = 𝑥2
− 6𝑥
5. If a certain growth of bacteria depends upon the formula 𝑦 = 200(4𝑥), what is 𝑦
when 𝑥 = −2?
A. 23.5
B. 22.5
C. 12.5
D. 11.5
6. What is 𝑓(𝑥) = 2−𝑥
if 𝑥 = −3 ?
A. 8
B. 6
C.
1
6
D.
1
8
t
e
t
f 018
.
0
2
.
14
)
( =

21. 19
7. A barangay has 1,000 individuals and its population doubles every 60 years.
What is the barangay’s population in 10 years?
A. 1,008
B. 1,020
C. 1,122
D. 1,182
8. The half-life of a substance is 400 years. What is the exponential model for
this situation if the initial amount is 200 mg?
A. 𝑦 = 200 (
1
2
)
400
𝑡
B. 𝑦 = 200 (
1
2
)
𝑡
400
C. 𝑦 = 400 (
1
2
)
𝑡
400
D. 𝑦 = 400 (
1
2
)
400
𝑡
9. Php 10,000 is invested at 2% compounded annually. What is the exponential
model for this situation?
A. 𝑦 = 10,000(2)𝑡
B. 𝑦 = 10,000(1.02)𝑡
C. 𝑦 = 10,000(0.2)𝑡
D. 𝑦 = 10,000(0.02)𝑡
10.Which of the situations can be modeled by an exponential function?
A. A radioactive substance decays after t units of time.
B. An amount deposited by Nheytan in Landbank of the Philippines
earns a compounded interest of 7.5% yearly.
C. A certain culture of bacteria doubles every an hour.
D. All of the above
11.What is if ?
A. 25
B. 10
C.
1
5
D.
1
25
12.Myries invested P50,000 after graduation. If the average interest rate is 4.8%
compounded annually, what is the exponential model for the situation?
A. 𝐴 = 50,000(0.048)𝑡
B. 𝐴 = 50,000(1.048)𝑡
C. 𝐴 = 50,000(0.048)𝑡
D. 𝐴 = 50,000(1.048)𝑡
13.The half-life of a substance is 400 years. How much will remain after 600
years if the initial amount was 200 grams?
A. 70.71 grams
B. 68.49 grams
C. 63.97 grams
D. 59.07 grams
x
x
f 5
)
( = 2
−
=
x

22. 20
14.A certain culture of bacteria grows in number according to the function
(in thousands). After one hour how many bacteria are there?
A. 2
B. 7
C. 10
D. 25
15.The population of the Philippines can be approximated by the function
where x is the number of years since 1955
(e.g. at 1955). Use this model to approximate the Philippine population
during the 1985. Round off answer to the nearest thousand. (Hint: use a
scientific calculator).
A. 42,467,211
B. 44,762,121
C. 46,117,422
D. 47,211,426
Additional Activity
Activity 5
Use a scientific calculator to answer this activity.
A large slab of meat is taken from the refrigerator and placed in a pre-heated
oven. The temperature T of the slab t minutes after being placed in the oven is given
by degrees Celsius. Construct a table of values for the following
values of t: 0, 10, 20, 30, 40, 50, 60, and interpret your results. Round off values to
the nearest integer.
t
N 5
2
=
x
.
e
P(x) 0251
0
000
,
000
,
20
= )
40
0
( 
 x
0
=
x
t
e
T 006
.
0
165
170 −
−
=

23. 21
Answer Key
What
Can
I
Do
1.
B
2.
millions
Assessment
1.
D
2.
B
3.
D
4.
C
5.
B
6.
A
7.
C
8.
B
9.
B
10.D
11.D
12.D
13.A
14.C
15.A
Additional
Activity
The
slab
of
meat
is
increasing
in
temperature
at
roughly
the
same
rate
What's
More
A.1
1.
Exponential
Equation
2.
Exponential
Inequality
3.
Exponential
Function
4.
None
of
these
5.
Exponential
Inequality
A.2
100,
10,
0.1,
1,
0.01
,
,
1,
3,
9
,
,
1,
,
A.3
1.
2.
3.
What
I
Know
1.
A
2.
C
3.
B
4.
D
5.
C
6.
A
7.
C
8.
B
9.
B
10.D
11.D
12.D
13.A
14.C
15.A
What
I
have
learned
1.
or
2.
Transformation
3.
population
growth,
decay
of
radioactive
substances,
compound
interest
offered
by
banks.
4.
5.
Half-life;
6.
7.
natural
exponential
function;

24. 22
References
1. Department of Education-Bureau of Learning Resources (DepEd-BLR) (2016)
General Mathematics Learner’s Material. Lexicon Press Inc., Philippines
2. Department of Education-Bureau of Learning Resources (DepEd-BLR) (2016)
General Mathematics Teacher’s Guide. Lexicon Press Inc., Philippines
3. Jose-Dilao, S. & Orines, F.B. (2009). Advanced Algebra, Trigonometry and
Statistics. SD Publications, Inc., Quezon City, Philippines
4. Fernandez, P.L, et. Al. (2007). A Course in Freshman Algebra. Ateneo de
Manila University Press, Quezon City, Philippines

25. DISCLAIMER
This Self-learning Module (SLM) was developed by DepEd SOCCSKSARGEN
with the primary objective of preparing for and addressing the new normal.
Contents of this module were based on DepEd’s Most Essential Learning
Competencies (MELC). This is a supplementary material to be used by all
learners of Region XII in all public schools beginning SY 2020-2021. The
process of LR development was observed in the production of this module.
This is version 1.0. We highly encourage feedback, comments, and
recommendations.
For inquiries or feedback, please write or call:
Department of Education – SOCCSKSARGEN
Learning Resource Management System (LRMS)
Regional Center, Brgy. Carpenter Hill, City of Koronadal
Telefax No.: (083) 2288825/ (083) 2281893
Email Address: region12@deped.gov.ph