Exponential Growth

THANK YOU!CORRECTCongratulations!Job well done.

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.

3How do bacteria multiply?

www.wadsworth.org 4Demonstrating Exponential Growth

fym.la.asu.edu www.ultimatedisney... www.sd4history.com 5ANOTHER EXAMPLE OF EXPONENTIAL GROWTH

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More examples of exponential growth

multi-level networking

social networkingcompound interest

7In Your Own Words , DefineEXPONENTIAL GROWTH1.

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8Recall Exponential FunctionDefinition: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.9Sample 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 later

image.spreadshirt...10Solution: 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. 11Another Form of Exponential FunctionThe Exponential Growth is in the formy = 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)12Example 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.uk13Solution: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) = 215,378Therefore after 3 years, the population will be 215,378.14Compound 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.aspwww.mahalo.com/answers/money/h15Tasks: 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 .YearSimple InterestCompound InterestPrincipalInterestFinal AmountPrincipalInterestFinal Amount12345

16 Graph YEARFINAL

AMOUNT17YearSimple InterestCompound InterestPrincipalInterestFinal AmountPrincipalInterestFinal Amount12000100210020001002100220002002200210010522053200030023002205110.252315.254200040024002315.25

115.762431.015200050025002431.01

121.552552.561015202518 GraphFINAL

AMOUNT YEAR1919

Questions1. 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 interestb. compound interest

20More Questions3. 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?

21Explain in your own words what the Narrator means by His Moral StoryEarn compound interest.Dont pay it.22Formula 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)23Number 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)24Example No.3Mr. 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-annuallyb. quarterly

c. monthly cdn4.wn.com

25Solution 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) = 580,270.4126b. 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 monthlyA = 500,000(1+.03/12)12(5) = 500,000(1.0025)60 = 580,808.3927Any Question?Based on the given example, which scenario or method of compounding will yield a higher interest?2828EvaluationThree 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?

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WORKSHEETNAMES:_______________________________DATE:_____________________________ & _______________________________YEAR & SEC. _______________________ Sammy deposited $2000 in a bank that pays 5% per annum.I. 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

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GRAPH OF SIMPLE INTEREST AND COMPOUND INTEREST

30000FINALAMOUNT

10000150002000025000 5000 12 3 4 5

LEGEND:SIMPLE INTEREST COMPOUND INTEREST Y E A R II. Answer the following questions:

1. Describe the changes in the simple interest and the compound interest as the period of time increases. ________________________________________________________________2. Based on your graph, is there a big difference between the simple interest and compound interest after 5 years. ________________________________

II. Try to continue the table by filling along 10,15,20 and 25 years using the formula for Exponential Growth (Party) for Compound Interest and also continue the graph from 5 to 25 years.3. Based on the new graph, 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 ____________________ 4. If the interest rate increases, what can you observe from the balance -year graph ? _________________________________________________________

5. 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? _____________________________

III. Discuss with your partner the moral of the story in the video. Earn compound interest. Dont pay it.

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NAME: ________________________YEAR & SEC. _______________

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?

Solution:1.

Solution:2. www.econofix.com

Solution: 3.cdn4.wn.com