Solve Gompertz Model for Population Growth with Help | TIA

[rroy81]

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.

 

[Mute]

What have you tried so far?

 

[rroy81]

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!

 

[Mute]

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?

 

[blue_raver22]

Hello,

Thank you for reaching out for assistance with solving the Gompertz model for population growth. This model is commonly used in population biology to describe the growth of a population over time.

To solve the Gompertz model for population growth, we will need to use the given equation: dy/dt = -ryln(y/k), where r = 0.67 per year and K = 36500 kg.

To find the predicted value of y(4), we will substitute t=4 into the equation and solve for y. This will give us the predicted population size after 4 years.

dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500)
dy/dt = -0.67 * y * ln(y/36500