1) The document discusses exponential growth functions and how changing the parameters a, h, and k transforms the graph of the exponential function f(x) = abx-h + k.
2) It explains that changing a stretches or compresses the graph vertically, changing h shifts the graph left or right, and changing k shifts the graph up or down.
3) Examples are given of exponential growth scenarios involving bacteria reproduction and how changes to the starting amount, time, or vertical shift would be represented by transformations to the parameters a, h, and k.
This talk is going to cover some techniques of counting using a computer. Counting problems come up very often in areas of databases, networking, and elsewhere. Counting is so simple that by itself it isn’t even worth talking about, but there are some techniques that have truly impressive gains.
Notes accompanying these slides: http://www.slideshare.net/roshmat/counting-using-computer
This talk is going to cover some techniques of counting using a computer. Counting problems come up very often in areas of databases, networking, and elsewhere. Counting is so simple that by itself it isn’t even worth talking about, but there are some techniques that have truly impressive gains.
Notes accompanying these slides: http://www.slideshare.net/roshmat/counting-using-computer
Los mejores profesionales inmobiliarios de toda España se reunieron el 12 y 13 de Junio de 2015 para compartir las últimas tendencias, las mejores ideas, lo que funciona y lo que ya no sirve para afrontar los mercados actuales. No seas el último en enterarte.
Este es un resumen fotográfico de los mejores momentos del evento.
UCI Hipotecas - Inmocionate 2015 (Cóctel)UCI España
Los mejores profesionales inmobiliarios de toda España acudieron a esta reunión anual donde se compartieron las últimas tendencias, las mejores ideas, lo que funciona y lo que ya no sirve para afrontar los mercados actuales.
Temas sobre los que se trató:
- La organización del negocio
- Cómo trabajan con las propiedades bancarias
- Las redes sociales
- El marketing online
- Las herramientas informáticas
- Etc
Have you had a formal or professional training on Technical Report writing before?
Have you experienced any difficulties to put your work, ideas & proposals in writing, professionally?
Have you had any of your reports being rejected or not understood?
Have you always wanted to impress your readers & superiors with a clear and professional report?
Effective Technical Report Writing will provide you with the exact skills to write technical reports and proposals that are informative, persuasive, clear and professional.
Contact Kris at kris@360bsi.com for further details.
NCV 3 Mathematical Literacy Hands-On Support Slide Show - Module 3Future Managers
This slide show complements the learner guide NCV 3 Mathematical Literacy Hands-On Training by San Viljoen, published by Future Managers. For more information visit our website www.futuremanagers.net
Los mejores profesionales inmobiliarios de toda España se reunieron el 12 y 13 de Junio de 2015 para compartir las últimas tendencias, las mejores ideas, lo que funciona y lo que ya no sirve para afrontar los mercados actuales. No seas el último en enterarte.
Este es un resumen fotográfico de los mejores momentos del evento.
UCI Hipotecas - Inmocionate 2015 (Cóctel)UCI España
Los mejores profesionales inmobiliarios de toda España acudieron a esta reunión anual donde se compartieron las últimas tendencias, las mejores ideas, lo que funciona y lo que ya no sirve para afrontar los mercados actuales.
Temas sobre los que se trató:
- La organización del negocio
- Cómo trabajan con las propiedades bancarias
- Las redes sociales
- El marketing online
- Las herramientas informáticas
- Etc
Have you had a formal or professional training on Technical Report writing before?
Have you experienced any difficulties to put your work, ideas & proposals in writing, professionally?
Have you had any of your reports being rejected or not understood?
Have you always wanted to impress your readers & superiors with a clear and professional report?
Effective Technical Report Writing will provide you with the exact skills to write technical reports and proposals that are informative, persuasive, clear and professional.
Contact Kris at kris@360bsi.com for further details.
NCV 3 Mathematical Literacy Hands-On Support Slide Show - Module 3Future Managers
This slide show complements the learner guide NCV 3 Mathematical Literacy Hands-On Training by San Viljoen, published by Future Managers. For more information visit our website www.futuremanagers.net
* Evaluate exponential functions.
* Find the equation of an exponential function.
* Use compound interest formulas.
* Evaluate exponential functions with base e.
Writing and solving equations can be abstract and confusing for students. Learn nonconventional ways to encourage flexible thinking and develop a deeper understanding of inverse relationships, fact families, and variables representation. Walk away with three easy-to-use activities to expand students' toolkit for solving equations.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
2. 1) Explain what a savings account is?
2) Why would someone want to have a savings account (as
opposed to a checking account)?
A major reason for having a savings account is that the interest rate
on a savings account is generally higher then a checking account.
Question:
What is interest?
3. Interest is basically the cost of money.
I want to burrow $23,000 from you, money which I don’t have, to buy a car.
Unless you have a generous and very rich family member, $23,000 isn’t money
that is just lying around.
However, you can burrow $23,000 from a bank. In return for the money the bank
gives you, you pay a little bit (or a lot) extra when you pay back the money.
The extra money you pay is called interest.
6. How much is in Fry’s bank account? Without calculating:
1) Make a guess
2) Give a value that you know for sure is too low
3) Give a value you know for sure is too high
4) Now answer question 1 and 2 in the ‘exponential growth’ worksheet
7. Exponential Growth is when a quantity grows by the same rate over
the same time period.
For example, Fry’s bank account grows by 2.25% every year (over the
course of 1000 years).
Rather then, calculate year-by-year to find the balance, you can write a
formula:
To calculate exponential growth you can use the function:
𝒇 𝒕 = 𝒂(𝟏 + 𝒓) 𝒕
a = original amount
r= rate of growth
t = time
Question: Think back to geometric sequences. Why is the common
ratio, r,(1+r) for exponential growth?
9. In the last example, we looked at interest that was accumulated once per
year.
One time per year you take your current balance and multiply it by the
interest rate to get your new value.
However….
When a banks compete for your money, they offer interest that
accumulates twice per year, quarterly, and even continuously.
Compounding interest is interest that is earned over a defined period
of time. The equation is:
𝒇 𝒕 = 𝒂 𝟏 +
𝒓
𝒏
𝒏𝒕
a = original amount
r= rate of growth
t = time in years
n = number of times interest compounded per year
10. I get a $1000 graduation gift. Being a savvy investor I get a mutual fund
that pays 3.5% interest over a period of 5 years. The interest on the
mutual fund is compounded monthly. When I graduate college in 5
years, how much will my Mutual Fund be worth?
Things I know:
a = $1000 original amount
r = 0.035
n = 12 times per year
t = 5 years
𝑓 𝑡 = 𝑎(1 +
𝑟
𝑛
) 𝑛𝑡
𝑓 𝑡 = 1000(1 +
0.035
12
)12(5)
$1190.94
11. Another mutual fund offers all identical options. However, the interest is
compounded daily instead of monthly. How much will you earn if you go with
the second mutual fund?
Things I know:
a = $1000 original amount
r = 0.035
n = 365 (because this one is compounded daily)
t = 5 years
$1191.24
Notice that the difference between the two option is
less then $1. However, when you as an investor
have little two distinguish the two mutual funds by,
the logical better choice is to choose the one which
will give you more money in the long run.
…and all else being equal, the better choice is to
go with the option that has the greatest rate of
compounding.
13. Answer question #5 and #6 on the worksheet and submit.
Watch the video, then..
14.
15. Please download the Desmos app if you do not
already have it.
Open the Exponential Growth Function worksheet
and answer question #1 through #4.
16. Day 1- Learn about specific application of exponential
growth to interest rate with an equation.
Day 2- Learn about exponential growth as a function and
the relationship between the equation and the graph.
17. Last class we talked about the growth of Fry’s bank
account. After 1000 years, Fry’s original balance of $0.93
becomes 4.3 Billion Dollars.
The graph that represents Fry’s bank account growth each
year is given below.
The x-axis represents time in years
since the account was opened.
The y-axis represents the balance in
the account.
I graphed the function:
𝑓 𝑡 = 0.93(1 + 0.0225 ) 𝑡
In writing: Describe the graph in your
own words.
19. The parent function of an exponential growth function is defined as:
𝑓 𝑥 = 𝑏 𝑥 where |b| > 1
The general form of an exponential function is:
𝑓 𝑥 = 𝑎𝑏 𝑥−ℎ + 𝑘
Now Answer question #5 on the worksheet (all parts).
The graph used to compare
other graphs to
20. To find out what happens when the exponential parent functions is
transformed let’s suppose that we have a sample of bacteria that like to
double over a certain time.
𝑓 𝑡 = 2 𝑡 means one bacteria doubles every time interval. (say
every hour). This will be our parent function.
𝑓 𝑡 = 2(2) 𝑡
means we start with 2 bacteria instead and double it.
Since a = 2 here the graph of this new function is stretched
vertically by a factor of 2.
If instead we could cut a bacteria in half and it still reproduced at
the same rate, we would start with a=0.5. This would compress
the function vertically by a factor of ½.
21. 2(2) 𝑥 (2) 𝑥
0.5(2) 𝑥
Notice y-values
when x=1 for all
three graphs here.
22. Now suppose that we have 2 bacteria but half of them die BEFORE they start
to double because of a freeze.
𝑓 𝑡 = 2(2) 𝑡−1 means we start with 2 bacteria and half of them die before
time starts.
Here h = 1, this has the effect of shifting your graph to the right 1
Now suppose the 2 bacteria already doubled before time starts (super
bacteria). In order to adjust, we need to make h= -1 (think of it as 1
hour before normal functions) which has the effect of shifting the graph
to the left 1 unit.
Another way to think of h is it’s ability to exponentially increase or
decrease your original starting amount by the common ratio (the b-
value).
If I start with 2 bacteria and h=2, my starting amount would be at
1/2 of a bacteria.
23. 2(2) 𝑥+1 2(2) 𝑥
2(2) 𝑥−1
Notice the x-values when
y=2 here.
24. Finally suppose you put another bacteria in before they start reproducing.
The function 𝑓 𝑡 = 2(2) 𝑥 + 1 means we put in an extra bacteria
Here k =1. This has the effect of shifting the graph up 1 unit.
Suppose instead you take one bacteria out (or one dies) before
they start to reproduce. Here k = -1 and this has the effect of
shifting the graph down one unit.
25. 2(2) 𝑥 − 1
2(2) 𝑥
2(2) 𝑥 + 1
Notice the y-values when
x=0