Answered

Find answers to your questions faster and easier with IDNLearn.com. Get thorough and trustworthy answers to your queries from our extensive network of knowledgeable professionals.

The number N(t) of people in a community who are exposed to a particular advertisement is governed by the logistic equation. Initially, N(0) = 200,and it is observed that N(1) = 400. Solve for N(t) if it is predicted that the limiting number of people in the community who will see the advertisement is 20,000. (Round all coefficients to four decimal places.)n(t) = ?

Sagot :

Sqdancefanidn

9514 1404 393

Answer:

  n(t) = 20,000/(1 +99e^(-0.7033t))

Step-by-step explanation:

One way to write the logistic function is ...

  n(t) = L/(1 +a·e^(-kt))

where L is the maximum value and parameters 'a' and k depend on boundary conditions.

Here, we have n(∞) = L = 20,000 and n(0) = L/(1+a) = 200. We also have n(1) = L/(1+a·e^-k) = 400.

Solving for 'a', we get ...

  n(0) = 20000/(1+a) = 200

  20000/200 -1 = a = 99

Solving for k, we get ...

  n(1) = 20000/(1 +99e^-k) = 400

  20000/400 -1 = 99e^-k = 49

  e^-k = 49/99

  k = -ln(49/99) ≈ 0.7033

So, the desired function is ...

  n(t) = 20000/(1 +99e^(-0.7033t))

View image Sqdancefan
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.