Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Let N* be the total number of ranchers in Uruguay, and N(t) be the number of ranchers who have adopted an improved pasture technology there. Assume that the rate of adoption, , is proportional to both the number who have adopted the technology and the fraction of the ranchers who have not (and so are susceptible to conversion). Let a be the proportionality constant.

a. Write down the differential equation modeling N(t).
b. According to Banks (1993), N* = 17000, N(0) = 170, a = 0.5 per year.

Determine how long it takes for the improved pasture technology to spread to 80% of the population of the ranchers.

Sagot :

batolisis

Answer:

A) dN / dt = aN( N* - N ) /N*

B) 12 years

Step-by-step explanation:

attached below is a detailed description of the solution

A) Write down the differential equation modelling N(t)

The differential equation of the modelling = dN / dt = aN( N* - N ) /N*

B) Determine how long it takes for improved pasture technology to spread to 80% of the population of the ranchers

firstly we will resolve the ODE and apply partial fractions, integrate and exponentiate before inputting the given data. attached below is a detailed solution

View image batolisis
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.