Solve Gompertz Model for Population Growth with Help | TIA

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Discussion Overview

The discussion centers around solving the Gompertz model for population growth, specifically the differential equation dy/dt = -ryln(y/k) with given parameters. Participants are seeking assistance in finding the predicted value of y(4).

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant requests help in solving the Gompertz model for population growth, providing specific parameters for the equation.
  • Another participant inquires about the attempts made by the original poster to solve the problem, suggesting a focus on the differential equation.
  • A later reply expresses uncertainty about how to approach the problem and mentions a specific answer they believe is correct.
  • Another participant hints at the nature of the differential equation, noting its first-order, homogeneous, and nonlinear characteristics, and suggests that the absence of explicit time may provide insights into solving it.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are varying levels of understanding and approaches to solving the problem, with some expressing uncertainty and others providing hints.

Contextual Notes

There are limitations related to the original poster's understanding of solving the differential equation and the assumptions involved in applying the Gompertz model.

rroy81
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I need help in solving the following solution.
The Gompertz model has been used to model population growth.
dy/dt = -ryln(y/k), where r = 0.67 per year, K = 36500 kg,

Use the Gompertz model to find the predicted value of y(4) .

TIA.
 
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What have you tried so far?
 
Mute said:
What have you tried so far?

That's just it...I am not to sure how to tackle the problem. I know the answer is 31374 kg.

How do I get is what I need help with.

Thanks!
 
Have you tried solving the differential equation? Do you have any ideas about how you might try to solve it? I'll give you a hint: t does not appear explicitly, and it is a first-order, homogeneous (but nonlinear) equation for y(t). Does this give you any ideas?
 

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