Question: Suppose that 0 < y 0 < N. Let b = (N - y 0 )/y 0 , and let y(x) = N/(1 + be

Suppose that 0 < y₀ < N. Let b = (N - y₀)/y₀ , and let y(x) = N/(1 + be^-kx) for all x. Show the following.
(a) 0 < y(x) < N for all x.
(b) The lines y = 0 and y = N are horizontal asymptotes of the graph.
(c) y(x) is an increasing function.
(d) ((ln b)/k, N/2) is a point of inflection of the graph.
(e) dy/dx is a maximum at x0 = (ln b)/k.

Step by Step Solution

★★★★★

3.23 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a 0 y 0 N implies that y 0 0 N 0 and N y 0 0 Therefore Als... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Calculus With Applications Questions!

Find all vertical and horizontal asymptotes of the graph of the function. 1. f (x) = 6x2 / x + 3 2. f (x) = 2x2 + 5x -3 / x2 + 2 3. g (x) = x2 / x2 - 4 4. g (x) = x + 1 / x2 - 1 5. h (x) = 5x + 20 /...

Grand Lake Corporations accounting records show the following at year-end December 31, 2010: Purchase Discounts ....... $ 5,700 Freight-in ........... 8,400 Freight-out .......... 11,100 Purchases...

Let f: X Y be differentiable at x0 with derivative Df[x0], and let x be a vector of unit norm (||x|| = 1). Show that the directional derivative of f at x0 in the direction x is the value of the...

Kindly ask you to help me with this problem on linear algebra: 1 Linear Algebra Let A be a real, symmetric, n x n matrix. Prove the following (a)-(c) using the Spectral theorem: . (a) A can be...

3. Consider the mass-spring system modeled as: dx dt m We let X = B 2m' -kx B x" +2\x' +wx: and w = y for our differential equation. Let's 1 > w. (a) Find the solution to the differential equation....

22. [-/5 Points] DETAILS HUNTERDM3 3.2.004. MY NOTES ASK YOUR TEACHER Consider the following recurrence relation: if n = 0 P ( m ) = (5 . P (n - 1 ) + 1 ifn > 0. Prove by induction that P(n) = 5" - 1...

Define the contextual-equivalence relation ` M =ctx M0 : for pairs of PCF terms M, M0 , PCF types , and PCF type environments . [3 marks] (ii) For PCF terms M and N with respective typings ` M : and...

Consider time-harmonic electromagnetic fields in the domain z 0 of the form (a) Let y E TE (x, z = 0, t = 0) = E y (x). Determine the scalar function TE (k x ) and the vector function TE(k x ) so...

Paoatnn 1 Consider the bridge truss diagrannued below: Given a vector of edema] forces [what we call the \"data\" or the \"right hand side"] b on the bridge. we can compute the forces F1. F2. . .. ....

O C 124 I Bb Bb C S I Bb IX Sy C C compass2g.illinois.edu/bbcswebdav/pid-5541353-dt-content-rid-7.. J Apple 3 iCloud FARM & BE Bing E Microsoft Word - Docum.. 2/3 - 105% + 5. Let B >0 and let X 1 ,...

Enterprises Ltd. (LEL). The shares have a paid-up capital value and a cost of $75,000. She transferred these shares under section 85 to a holding company, Holdco Inc., which her two Canadian-resident...

As a result of its export sales to customers in Switzerland, the Lenox Company has had Swiss franc denominated revenues over the past number of years. In order to gain protection from future exchange...

The Independence Standard Board ( ISB ) establishes responsibilities for the management: Management is responsible for financial statements, and responsibility for the choices and judgments inherent...

Refer to the EER diagram for patients in Figure 3-3. Make any assumptions you believe are necessary. Develop sample definitions for each entity type, attribute, and relationship in the diagram.

Solve each quadratic inequality. Graph each solution. 3x 2 + 2x > 1

Solve each quadratic inequality. Graph each solution. 10r 2 + r 2

Solve each quadratic inequality. Graph each solution. x 2 4x 5

All else equal, what will the yield of a bond rated A- be relative to a bond rated BBB+? Multiple Choice O Higher Yield Lower Yield Same Yield. A bond with a coupon rate of 9.5%, that pays coupons...

Sharp Products, Inc. seeks a potential expansion into solar heating. Sharp has hired you to help them compute estimates of the appropriate after-tax WACC for assessing new solar heating projects....

Bond A has an 11% annual coupon, matures in 12 years, and has a $1,000 face value. Bond B has a 13% annual coupon, matures in 12 years, and has a $1,000 face value. Bond C has a 9% annual coupon,...