Graphs of logistic functions (Figures 2 and 3) look suspiciously similar to the graph of the hyperbolic

Question:

Graphs of logistic functions (Figures 2 and 3) look suspiciously similar to the graph of the hyperbolic tangent function. Explain the similarity by showing that the logistic function given by Equation 7 can be written as

Where c = (ln A) / k. Thus the logistic function is really just a shifted hyperbolic tangent.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0538497909

7th edition

Authors: James Stewart

See More Books

Question Posted: Mar 04, 2016 07:15 AM

See More Questions

Graphs of logistic functions (Figures 2 and 4) look suspiciously similar to the graph of the hyperbolic tangent function (Figure 3 in Section 3.9). Explain the similarity by showing that the logistic...
The graphs of two functions and g are shown in the figures. Find ( g)(2). y (3, 4) (4, 8) y = f(x) y = g(x) (2, 2) (2, 1) 4 (1, 1) 2.
The graphs of two functions and g are shown in the figures. Find (g f)(3). y (3, 4) (4, 8) y = f(x) y = g(x) (2, 2) (2, 1) 4 (1, 1) 2.
An investor utilizes a bull call spread by purchasing a call option for a premium of $10. The call option comes with a strike price of $50 and expires in July 2020. At the same time, the investor...
For each of the following, indicate whether the statement is true or false and include a brief explanation for your answer. a. A pension trust fund appears in the government-wide financial statements...
Explain how and why different communication styles and channels are influenced by various cultural types, such as participative or hierarchical cultures.
Two immiscible, incompressible, viscous fluids having the same densities but different viscosities are contained between two infinite, horizontal, parallel plates (Fig. P6.80). The bottom plate is...
You buy a share of The Ludwig Corporation stock for $21.40. You expect it to pay dividends of $1.07, $1.1449, and $1.2250 in Years 1, 2, and 3, respectively, and you expect to sell it at a price of...
1. What must be the betas of a portfolio with the following expected returns E (rp) = 18%, 8%, 28%, and 36%, if r = 4% and E(M) 14%? =
Chloe was hired to provide customer service training to the employees at CAB Inc. Chloe signed a contract stating that she was an independent contractor acting as a consultant. There was no fixed...
In a seasonal-growth model, a periodic function of time is introduced to account for seasonal variations in the rate of growth. Such variations could, for example, be caused by seasonal changes in...
The Pacific halibut fishery has been modeled by the differential equation dy/dt = ky(1 - y/M) Where y(t) is the biomass (the total mass of the members of the population) in kilograms at time...
For the beams shown in Figures P4-42 through P4-44, with internal hinge, determine the deflection at the hinge. Let E = 210 GPa and I = 2 10-4 m4. Figure P4-42 Figure P4-43 Figure P4-44 P = 5 KN...
(e) Find the volatility of the portfolio in (d). (f) Would anyone prefer stock A to the portfolio in (d)? Why or why not. Suppose that there are two assets: A and B. Asset A has expected return of...
a) Meta-Technetium-99 is a radioisotope commonly used in radiopharmaceutical applications. It is obtained from the decay of Molybdenum-99, which is itself produced artificially either by neutron...
Suppose that an economist hypothesizes that the annual quantity demanded of a specific computer brand (Q D ) is determined by the price of the computer (P) and the average income of consumers (Y)...
118. Match the following columns. Column-I Column-II A Ladybird () Methanobacterium B Mycorrhiza (II) Trichoderma C Biological control (III) Aphids D Biogas (IV) Glomus (1) A-2 B-4; C-3; D-1 (2) A-3;...
A family has the following housing costs: Annual Amount Paid on Mortgage: $17,791 Property Tax: $9,175 Homeowners' Insurance: $1,355 In addition, it pays out $9,860 annually on its car loan. Compute...
Which type of income statementsingle-step or multiple-stepdoes Shoppers Drug Mart use? You can find its financial statements in Appendix A at the back of this textbook.
White Bolder Investments (WBI) You are an intern working for WBI, a large investment advisory services in Sydney. Among other regular customers, WBI has been providing advisory services for Jumbo...
(a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and the inflection points.
Evaluate the limit. lim In x 1
Find the most general antiderivative of the function. 2 5 f(x)
What are non marginal investors? How can i distinguish between a non marginal investor and a marginal investor among shareholders? Explain it briefly and conclude it.
How would Stephanies decisions concerning conducting stock transactions be affected if she were 35 years old? If she were 50 years old? What are stock exchanges? How do they facilitate the trading of...
Write a script to determine whether a given file system or mount point is mounted, and output the amount of free space on the file system if it is mounted. If the file system is not mounted, the...

Graphs of logistic functions (Figures 2 and 3) look suspiciously similar to the graph of the hyperbolic

Question:

Po) = M[1 + tanh(kKe - )]

Step by Step Answer:

By Equation 7 Pt K 1 Ae kt By compari...View the full answer

Calculus Early Transcendentals

Students also viewed these Calculus questions