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EXPONENTIAL GROWTH
4th Year Level
Cristina P. David
ERNESTO RONDON HIGH SCHOOL
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Target Group: 4th Year Level
Duration : 50 minutes
Prerequisite Skill: ExponentialFunction
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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.
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DEMONSTRATING EXPONENTIAL GROWTH
fym.la.asu.edu
www.ultimatedisney... www.sd4history.com
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ANOTHER EXAMPLE OF EXPONENTIAL GROWTH
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MORE EXAMPLES OF EXPONENTIAL GROWTH
multi-level networking
social networking compound interest
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IN YOUR OWN WORDS , DEFINE
EXPONENTIAL GROWTH1.
2.
3.
4.
5.
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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.
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SAMPLE PROBLEMThe 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 laterimage.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)
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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
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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.
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COMPOUND INTEREST
Do watch the ffg. videos and take note how compound interest is computed compared to simple interest.
Compound Interest VS Simple Interest
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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 Compound Interest
Principal
Interest Final Amount
Principal Interest Final Amount
1
2
3
4
5
worksheet
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GRAPH
1 2 3 4 5 60
500
1000
1500
2000
2500
3000
Simple Interest
Compound In-terest
YEAR
FINAL
AMOUNT
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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
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1 4 7 10 13 16 19 22 250
1000
2000
3000
4000
5000
6000
7000
8000
Simple In-terest
GRAPH
FINAL
AMOUNT
YEAR
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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
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MORE QUESTIONS…
3. If the interest rate increases, what can you observe from the balance –year graph?
4. If the amount will be compounded semi-annually, what can you observe on the same graph?
Can we still use the same formula in no.2?
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EXPLAIN IN YOUR OWN WORDS WHAT THE
NARRATOR MEANS BY HIS MORAL STORY
Earn compound interest.
Don’t pay it.
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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)
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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)
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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
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ANY QUESTION?
Based on the given example, which scenario or method of compounding will yield a higher interest?
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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?
P
3% interest
compounded
annually
5 years
evaluation
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2%interest
P
n =4
3 years
2.5 %
interest
compo-undedmonthly
2years
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.
FIN
SORRY!SORRY!
CORRECTCongratulation
s!Job well done.
THANK YOU!
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