LESSON EXEMPLAR FOR MATHEMATICS IV
I. GRADING LEVELThis lesson is intended for Grade 10
students.
II. GRADING PERIOD3RD Grading Period
III. LEARNING COMPETENCIES Identify certain relationships in
real life which are exponential Define the exponential function ,
and differentiate it from other functions studied earlier, given a
table of ordered pairs, state whether the trend is exponential or
not.
IV. TIME3 sessions
V. TOPICDefinition and Form of Exponential FunctionVI.
ACTIVITY
Consider the problem below. Prepare a table showing the daily
salary of a worker under each option. Then, using only one
rectangular coordinate system, sketch their graphs.
Suppose you are at an interview for a job. While there, you are
asked which salary you would prefer. Salary A would pay Php200 for
the first day and give you a daily increase of Php50. Salary B
would pay Php1 for the first day and every successive day you will
be paid double the amount.
VII. Questions 1. Suppose the job will only last for 10 days,
which salary would give a higher profit? By how much?2. What if the
job will last for 13 days, which salary would you prefer A or B?
Why?3. What kind of function is represented by Salary A? If we let
n be the number of days elapsed and f(n) is the salary after n days
, form the respective equations of the two salary options.4.
Identify the function represented by Salary A? How about the
equation for Salary B, have you encountered it from the previous
functions studies earlier? It is an example of a new function,
called Exponential Function.5. Look at your table of values and
graphs, how would you differentiate linear function and exponential
function? Which one grows faster?
VIII. DISCUSSIONDiscuss with the class the table of values of
the two salary options as well as their graphs. Then using the
tables and graphs, discuss the answers of the given questions.After
the discussion of the activity, present to the class the form and
definition of exponential function, then give additional examples
of equations representing exponential functions. Give also some
counter examples. Then put on view the simplest form of linear
function y = x , quadratic function y = x2 and exponential function
y = 2x with their table of values and graphs, and then guide
students in differentiating these functions as regards table
properties, and graph properties.
IX. ASSESSMENTChoose the letter of the correct answer.1. Which
of the following graphs represent an exponential trend?a. b. c.
d.
2. Which of the following equations is not an exponential
function?a.
3. What is the trend of the , when 0 < a < 1 ?a.
increasingb. decreasing c. constant d. cannot be determined
4. Which of the following table of values shows an exponential
trend?x-4-3-2-10
y29191151
x01234
y-1-3-9-27-81
c. a.
x-1-2-3-4-5
55555
x246810
y1015202530
d. b.
5. Which of the following life-like situations exhibit an
exponential pattern?a. A convenience store has 50 customers and
each week 2 new customers are comingb. A rubber ball is dropped
from a height of 20 meters. It rebounds one third of the distance
it has fallen after each fall.c. A vegetable plantation watered at
a fixed rate of 150 liters per hour through a water pump. d. The
area of a rectangle with length equal to two more than its
width.
AUTHOR:WINNIE W. POLIPOSITION:MASTER TEACHER 1SCHOOL: MUOZ
NATIONAL HIGH SCHOOLDIVISION:SCIENCE CITY OF MUOZ
