To graph: the given function and find the y -intercept and the horizontal asymptote.
y -intercept −
Horizontal asymptotes are
Given information:
The given function is
Definition Used:
Logistic Growth Function:
Let a , b , c , and k be positive constants, with
Where the constant c is the limit to growth.
Explanation:
To graph the given function using Ti-83 calculator,
First pressand enter the function as shown:
Then press and set the window as shown:
Lastly press and this gives the required graph.
Now, to find the y -intercept substitute
So, y- intercept is
By the above definition, the numerator of a logistic growth function is known as its limit to growth. Since, for any logistic growth function f ( x ),
and thus
Here, the numerator of the given function is 9.
So,
Also, every logistic growth function will approach zero as x tends to negative infinity, that is, for a logistic growth function f ( x ),
and thus
Chapter 3 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning