View by Category

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – Exponential Growth PowerPoint presentation | free to view - id: 1ce025-ZDc1Z

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Exponential Growth DecaySection 4.5

- JMerrill, 2005
- Revised 2008

Review

Is this okay?

NO

Arguments must be positive

Review

500e0.3x 600 e0.3x 1.2 ln 1.2 0.3x

x 0.608

Exponents and Logarithms

- How are exponents and logarithms related?
- They are inverses of each other
- Why is this important?
- Using inverses allow us to solve problems (we use

subtraction to solve addition problems division

to solve multiplication) - Many real-life scenarios are exponential in

nature and logarithms allow us to solve for the

unknown.

Examples Using Logarithmic Scales

- The Richter scale is used to determine the

intensity of an earthquake. - Measuring acidity using the pH scale, or

concentration of ions. - Carbon dating.
- Modeling population growth/decay--just to name a

few

Exponential Decay Model

- A(t) A0ekt
- A0 is the initial amount
- K is the growing/decay entity. If kgt0, the

entity is growing (an increasing function). If

klt0, the entity is decaying (a decreasing

function). - Looks like A(t) Pert? It works the same way.

Population Model

- In 1970, the US population was 203.3 million. In

2003, the population was 294 million. - Find the exponential growth model
- By which year will the US population reach 315

million?

Population Model

- t is the number of years after 1970.
- t0 represents 1970. t 33 represents 2003
- When t 33, A 294
- A(t) A0ekt
- 294 203.3ek(33)

Population Cont

What do you do when the exponent is a variable?

- 294 203.3ek(33)

So, k 0.011, which is exponential growth

The growth model is A(t) 203.3e0.011t

What does lne ?

Population Cont

- When will the population reach 315 million?
- A(t) 203.3e0.011t
- 315 203.3e0.011t
- You finish
- Did you get approximately 40?
- That means that in the year 2010 the population

will be approx. 315 million!

Carbon Dating

- The natural base, e, is used to estimate the ages

of artifacts. Plants and animals absorb

Carbon-14 from the atmosphere. When a plant or

animal dies, the amount of carbon-14 it contains

decays in such a way that exactly half of the

initial amount is present after 5,715 years.

Carbon Dating

- The function that models the decay of carbon-14,

where A0 is the initial amount of carbon-14, and

A(t) is the amount present t years after the

plant or animal dies, is

Carbon Dating Example

- Archaeologists find scrolls and claim that they

are 2000 years old. Tests indicate that the

scrolls contain 78 of their original carbon-14.

Could the scrolls be 2000 years old? - Using the same process as the last example, we

find k to be -0.00012. - Finding k is written out in the book on P449.

Carbon Dating Example

78 of the original amount

You Do

- A wooden chest is found and said to be from the

2nd century BCE. Tests on a sample of wood from

the chest reveal that it contains 92 of its

original carbon-14. Could the chest be from the

2nd century BCE? - Use the same k as the last example.

You do

Logistic Growth Model

- The spread of disease is exponential in nature.

However, there arent an infinite number of

people. Eventually, the disease has to level

off. Growth is always limited. A logistic

growth model is used in this type of situation - Y c is the horizontal asymptote. Thus c is the

limiting value of the function.

Modeling the Spread of the Flu

- The function below describes the number of

people, f(t), who have become ill with influenza

t weeks after its initial outbreak in a town with

a population of 30,000 people.

Modeling the Spread of the Flu

- How many people became ill with the flu when the

epidemic began? - How many people were ill by the end of the fourth

week? - What is the limiting size of f(t), the population

that become ill?

Modeling the Spread of the Flu

- How many people became ill with the flu when the

epidemic began? - In the beginning, t 0

Modeling the Spread of the Flu

- 2. How many people were ill by the end of the

fourth week?

Modeling the Spread of the Flu

- 3. What is the limiting size of f(t), the

population that become ill?

C represents the limiting size that f(t) can

obtain. There are only 30,000 people in the

town, therefore, the limiting size must be 30,000!

About PowerShow.com

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2016 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2016 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Exponential Growth" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Ccccd University and other schools with their online training by sharing educational presentations for free