slide1
Download
Skip this Video
Download Presentation
6.5

Loading in 2 Seconds...

play fullscreen
1 / 13

6.5 - PowerPoint PPT Presentation


  • 128 Views
  • Uploaded on

6.5. Logistic Growth Model. Bears. Years. Greg Kelly, Hanford High School, Richland, Washington. We have used the exponential growth equation to represent population growth. The exponential growth equation occurs when the rate of growth is proportional to the amount present.

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 '6.5' - kane


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
slide1

6.5

Logistic Growth Model

Bears

Years

Greg Kelly, Hanford High School, Richland, Washington

slide2

We have used the exponential growth equation

to represent population growth.

The exponential growth equation occurs when the rate of growth is proportional to the amount present.

If we use P to represent the population, the differential equation becomes:

The constant k is called the relative growth rate.

slide3

The population growth model becomes:

A more realistic model is the logistic growth model where growth rate is proportional to both the amount present (P) and the fraction of the carrying capacity that remains:

However, real-life populations do not increase forever. There is some limiting factor such as food, living space or waste disposal.

There is a maximum population, or carrying capacity, M.

slide4

Logistics Differential Equation

The equation then becomes:

Our book writes it this way:

We can solve this differential equation to find the logistics growth model.

slide5

Partial

Fractions

Logistics Differential Equation

slide9

Example:

Logistic Growth Model

Ten grizzly bears were introduced to a national park 10 years ago. There are 23 bears in the park at the present time. The park can support a maximum of 100 bears.

Assuming a logistic growth model, when will the bear population reach 50? 75? 100?

slide10

Ten grizzly bears were introduced to a national park 10 years ago. There are 23 bears in the park at the present time. The park can support a maximum of 100 bears.

Assuming a logistic growth model, when will the bear population reach 50? 75? 100?

slide13

Bears

Years

We can graph this equation and use “trace” to find the solutions.

y=50 at 22 years

y=75 at 33 years

y=100 at 75 years

p

ad