exponential growth and decay n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Exponential Growth and Decay PowerPoint Presentation
Download Presentation
Exponential Growth and Decay

Loading in 2 Seconds...

play fullscreen
1 / 11

Exponential Growth and Decay - PowerPoint PPT Presentation


  • 93 Views
  • Uploaded on

Exponential Growth and Decay. Modified from the presentation at: www.mathisnothard.com/pages/.../ powerpoint s/exp growthdecay . ppt. E XPONENTIAL G ROWTH M ODEL. W RITING E XPONENTIAL G ROWTH M ODELS. C is the initial amount. t is the time period. y = C (1 + r ) t.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Exponential Growth and Decay' - spike


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
exponential growth and decay

Exponential Growth and Decay

Modified from the presentation at: www.mathisnothard.com/pages/.../powerpoints/expgrowthdecay.ppt

slide2

EXPONENTIAL GROWTH MODEL

WRITING EXPONENTIAL GROWTH MODELS

C is the initial amount.

t is the time period.

y = C (1 + r)t

(1 + r) is the growth factor,r is the growth rate.

you try
You Try:

Your business had a profit of $25,000 in 1998. If the profit increased by 12% each year, what would your expected profit be in the year 2010?

C = $25,000

T = 12

R = 0.12

slide4

Writing an Exponential Growth Model

A population of 20 rabbits is released into a wildlife region.

The population triples each year for 5 years.

What is the population after 5 years?

SOLUTION

After 5 years, the population is

P = C(1 + r)t

Exponential growth model

= 20 • 35

= 4860

There will be about 4860 rabbits after 5 years.

slide5

EXPONENTIAL DECAY MODEL

WRITING EXPONENTIAL DECAY MODELS

C is the initial amount.

t is the time period.

y = C (1 – r)t

(1 – r) is the decay factor,r is the decay rate.

example depreciation
Example: Depreciation
  • You buy a new car for $22,500. The car depreciates at the rate of 7% per year,
  • What was the initial amount invested?
  • What is the decay rate? The decay factor?
  • What will the car be worth after the first year? The second year?
  • The initial investment was $22,500.
  • The decay rate is 0.07. The decay factor is 0.93.
you try1
You Try:

Iodine-131 is a radioactive isotope used in medicine. Its half-life or decay rate of 50% is 8 days. If a patient is given 25mg of iodine-131, how much would be left after 32 days or 4 half-lives.

C = 25 mg

T = 4

R = 0.5

slide8

Continuous Compounding

  • We can compound every instant (i.e., continuously):
  • Here, F is the future value, P is the present value, r is the annual rate of interest, t is the total number of years, and e is a constant equal to about 2.718

clem.mscd.edu/~mayest/FIN3300/Files/ch5.ppt

slide9

Example:

  • Suppose that the Fourth National Bank is offering to pay 10% per year compounded continuously. What is the future value of your $1,000 investment?

clem.mscd.edu/~mayest/FIN3300/Files/ch5.ppt

slide10

Example:

  • Suppose that the Fourth National Bank is offering to pay 10% per year compounded continuously. If you plan to leave the money in the account for 5 years, what is the future value of your $1,000 investment?

clem.mscd.edu/~mayest/FIN3300/Files/ch5.ppt

homework
Homework

p.456,

#4, 5, 6, 8, 9, 12