   Chapter 2.4, Problem 12E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 11-16, choose the logistic function that best approximates the given curve. (A) f ( x ) = 8 1 + 7 ( 2 ) − x (B) f ( x ) = 8 1 + 3 ( 2 ) − x (C) f ( x ) = 6 1 + 11 ( 5 ) − x

To determine

The correct logistic function f

from the given choices for the following curve, (A). f(x)=81+7(2)x

(B). f(x)=81+3(2)x

(C). f(x)=61+11(5)x

Explanation

Given Information:

The provided curve is,

The given choices for the correct logistic function are,

(A). f(x)=81+7(2)x

(B). f(x)=81+3(2)x

(C). f(x)=61+11(5)x

The form of the logistic function is:

f(x)=N1+A(bx)

Where constants N,A

and b

are non-zero (A,bare positive and b1).

There are certain properties of the curve represented by the logistic curve, y=N1+A(bx)

1.

The graph of the function formed is S-shaped which is formed by sandwiching between the horizontal lines y=0 and y=N, which means the limiting value of the function is N.

2.

If b>1, graph rises, if b<1, the graph falls.

Now, the provided curve is,

It is clear from the curve that the function f

has limiting value 8, which means the value of constant N=8

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