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 16.
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.
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