Question: The Gompertz growth equation is where a and b are positive constants. This equation is used in biology to describe the growth of certain populations.

The Gompertz growth equation is dy dt = -ay In b'

where a and b are positive constants. This equation is used in biology to describe the growth of certain populations. Find the general form of solutions to this differential equation. (Figure 8 shows several solutions corresponding to a = .04 and b = 90.)

dy dt = -ay In b'

Step by Step Solution

★★★★★

3.45 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

dy dt ay In VI v 0 b inm y b ... 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 Applied Calculus Questions!

Solve the preceding problem if the mass of the tail gate is MT = 27 kg and that of the crate is MC = 68 kg. Use dimensions H = 305 mm, L = 406 mm, dC = 460 mm, and dT = 350 mm. The cable...

The rate at which a drug is absorbed into the bloodstream is modeled by the first-order differential equation dC/dt = a - bC(t) Where a and b are positive constants and C(t) denotes the concentration...

The differential equation dx/dt = x(a - b ln x) where x represents the number of objects at time t, and a and b are constants, is the model for Gompertz curves. Recall from Section 5.3, "Solutions of...

The relation between the tension T and the steady shortening velocity v in a muscle is given by the Hill equation: (T + a)(v + b) = (T0 + a)b where a and b are positive constants and T0 is the...

The Gompertz equation was first derived in 1825 and is now often used to model populations, particularly of tumour cells. One well-known example of this is the work of Anna Laird, who was one of the...

Fraction of hosts infected Case Study 2 Hosts, Parasites, and Time-Travel 0.8 0.6 0.4 0.2 0 Past Contemporary Future Time Figure \u00031 Horizontal axis is the time from which the parasite was taken,...

( technology forecasting) can u tell me what method/ model used in this report, need only two. choose from this one https://pdfs.semanticscholar.org/fede/a35685428f15a3a7a32db5b96f232e0dcda3.pdf?_ga=...

2.7. Explicit Solutions to Dierential Equations 109 power (kw) 20 15 10 5 0 08:00 10:00 12:00 14:00 16:00 time 18:00 2.7 Explicit Solutions to Dierential Equations In the very rare case in which an...

Set Student Name: 1. Describe the relationship between two variables that have a correlation coefficient value: a. Near -1 b. Near 0 c. Near 1 2. Data was collected where a weightlifter was asked to...

Instuctor's Annotated Edition TENTH EDITION Understandable Statistics Concepts and Methods Charles Henry Brase Regis University Corrinne Pellillo Brase Arapahoe Community College Australia Brazil...

What is the relationship between ethics and law?

The common rule throughout the US is that individuals are not breaching a duty of care to come to someone's rescue if another person is in need of help. However, once any form of aid is rendered,...

E12.15 (LO 2) (Restructuring Issues) EADS Ltd. is involved in a restructuring related to its energy division. The company controller and CFO are considering the following costs to accrue as part of...

Consider the following two earnings forecasting models: E,(EPS) is the expected forecast of earnings per share for year t+1, given informa- tion available at t. Model 1 is usually called a random...

A biology student finds that of 35 males with Drosophila melanogaster, 2 have Adh genotypes with a male mating advantage. (a) Using the standard methods, find a 95% confidence interval for the true...

A semiconductor manufacturer collects data from a new tool and conducts a hypothesis test with the null hypothesis that a critical dimension mean width equals 100 nm. The conclusion is to not reject...

The standard deviation of critical dimension thickness in semiconductor manufacturing is = 20 nm. (a) State the null and alternative hypotheses used to demonstrate that the standard deviation is...

CALGARO EREK NEXT Multiple Choice Question 122 The following credit sales are budgeted by Concord Corporation: January $124000 February 230000 March 350000 270000 The company's past experience...

Part a.) X Corp. (an U.S. based corporation) has the following operating incomes (i.e., taxable income not including any net operating loss deduction) for the following years: 2014 2015 2016 2017...

Stock X is selling for $45. The cost of equity is 14% and Stock X just paid a $5 dividend to shareholders. Use the Constant-Growth Dividend Discount Model to solve for g and estimate the...