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EXPONENTIAL GROWTH
4th Year Level
Cristina P. David
ERNESTO RONDON HIGH SCHOOL
Target Group: 4th Year Level
Duration : 50 minutes
Prerequisite Skill: Exponential
Function
2
OBJECTIVES:
At the end of the lesson, the students
shall be able to:



Define exponential growth
Differentiate between simple and
compound interest
Compute for the final amount of
compound interest and population growth.
3
HOW DO BACTERIA
MULTIPLY?
4
www.wadsworth.org
DEMONSTRATING
EXPONENTIAL GROWTH
fym.la.asu.edu
5
www.ultimatedisney...
www.sd4history.com
ANOTHER EXAMPLE OF
EXPONENTIAL GROWTH
6
MORE EXAMPLES OF EXPONENTIAL GROWTH
multi-level networking
social
networking
7
compound interest
IN YOUR OWN WORDS , DEFINE
EXPONENTIAL GROWTH
1.
2.
3.
4.
5.
8
RECALL EXPONENTIAL FUNCTION
Definition:
If b>0 and b ≠ 1, and k is a constant,
then y = kbx , where x is a real
number, is called an exponential
function with base b.
9
SAMPLE PROBLEM
The number of bacteria in a culture
is given by the function
y= 50(2t) where t is the number of
hours after the start of observation.
Find the number of bacteria in the
culture :
a.) at the start of observation
b.) 3 hours later
image.spreadshirt...
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SOLUTION:
Given y = 50(2t)
a. At the start, t = 0. Putting t = 0 into the
function,
y = 50(20)
= 50(1)
= 50
hence the number of bacteria at the start is 50.
b.
When t = 3
y = 50 (23)
= 50 (8)
= 400
hence the number of bacteria after 3 hours is 400.
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ANOTHER FORM OF
EXPONENTIAL FUNCTION
The Exponential Growth is in
the form
y = P( 1 + r)t
where P = original number or amount
r = rate of change
t = unit of time
y = total number or amount after
t years
( Party or Pretty)
12
EXAMPLE NO. 2
A certain city has a population of
200,000 and a growth rate of 2.5%.What
will be the expected population after 3
years?
telegraph.co.uk
13
SOLUTION:

Given:
P = 200,000
r = 2.5 % or .025
t = 3 yrs.
Find : y
Using the formula y = P( 1 + r)t and
substituting the given :
y = 200,000 ( 1.025)3
= 200,000 ( 1.076891)
= 215,378
Therefore after 3 years, the population will be
215,378.
14
COMPOUND INTEREST
Do watch the ffg. videos and take note how
compound interest is computed compared to
simple interest.
Compound Interest VS Simple Interest
www.nycon.org/joinus/index.asp
www.mahalo.com/answers/money/h
15
TASKS:
Sammy deposited $2000 in a bank that pays 5%
per annum.
Complete the table below and make a graph
showing the two kinds of interest .
Year
Simple Interest
Principal
Interest
Final
Amount
Compound Interest
Principal
Interest
Final Amount
1
2
3
4
5
16
GRAPH
F
I
N
A
L
A
M
O
U
N
T
3000
2500
2000
Simple Interest
1500
Compound Interest
1000
500
0
1
2
3
4
5
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YEAR
Year
Simple Interest
Compound Interest
Principal
Interest
Final
Amount
Principal
Interest
Final
Amount
1
2000
100
2100
2000
100
2100
2
2000
200
2200
2100
105
2205
3
2000
300
2300
2205
110.25
2315.25
4
2000
400
2400
2315.25
115.76
2431.01
5
2000
500
2500
2431.01
121.55
2552.56
10
15
20
25
18
GRAPH
F
I
N
A
L
8000
7000
6000
5000
Simple
Interest
Compound
Interest
4000
A
M
O
U
N
T
3000
2000
1000
0
1 3 5 7 9 11 13 15 17 19 21 23 25
YEAR
19
QUESTIONS
1. Describe the changes
in the simple
interest and the compound interest as the
period of time increases.
2. After how many years will the balance be
at least double the original principal if the
interest is calculated using :
a. simple interest
b. compound interest
20
MORE QUESTIONS…
3. If the interest rate increases, what can
you observe from the balance –year
graph?
4. If the amount will be compounded semiannually, what can you observe on the
same graph?
Can we still use the same formula in
no.2?
21
EXPLAIN IN YOUR OWN WORDS WHAT THE
NARRATOR MEANS BY HIS MORAL STORY
Earn compound
interest.
Don’t pay it.
22
FORMULA FOR COMPOUND INTEREST
Compound Interest Formula
A = P(1 + r/n)nt
where A = the final amount
P = principal
r = rate of interest
n = no. of compounding in a year
t = time or no.of years
(Apparent or A parent)
23
NUMBER OF COMPOUNDING IN A YEAR
A certain principal or deposit can be
compounded annually, semi-annually,
quarterly, monthly, bi-monthly or even
daily.
For a given kind of compounding in a
year, we use the ff. for the value of n:
n = 1 (annually or yearly)
n = 2 ( semi-annually or bi-annually)
n = 4 ( quarterly)
n = 12 ( monthly)
24
EXAMPLE NO.3
Mr. Sy deposited an amount of Php 500,000
at Banco De Oro which gives 3% interest
compounded annually. How much will be his
money after 5 years?
Compute for the final amount if the bank
will compound his money:
a. semi-annually
b. quarterly
c. monthly
cdn4.wn.com
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SOLUTION
a. Given: P = 500,000
r = 3% or .03
n=2
t=5
Find: A
To solve for A: Use the Apparent formula
A = P(1+r/n)nt
= 500,000(1+.03/2)2(5)
= 500,000(1.015)10
= 500,000(1.160541)
= 580,270.41
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b. Using the same given facts in (a) except for n.
Since compounding is done quarterly, n = 4.
To solve for A: (Use the same apparent formula)
A = 500,000(1+.03/4)4(5)
= 500,000(1.0075)20
= 500,000(1.161184)
= 580,592.07
c.Using n=12 since interest is compounded monthly
A = 500,000(1+.03/12)12(5)
= 500,000(1.0025)60
= 580,808.39
27
ANY QUESTION?
Based
on
the
given
example, which scenario or
method of compounding will
yield a higher interest?
28
EVALUATION
Three banks made the following offers to
their customers. If you are to deposit your money,
which of the following banks do you think will
give you the best deal?
compounded
annually
3% interest
5 years
P
29
2%
interest
3 years
P
n =4
2.5 %
interest
compounded
monthly
2
years
cdn4.wn.com
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ASSIGNMENT
1. Visit at least 3 banks nearest to your
community. (in a mall for example) and ask an
officer regarding the rate of interest and the
method of compounding.
2. Using a specific number of years and amount to
be invested or deposited, compare the final
amount and decide which bank offers the great
deal.
3. Ask your parent if they have a credit card or
have experienced obtaining a loan from a
lending institution and ask them the rate of
interest and how compounding is done.
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FIN