Explanation Approach: The formula for a logistic model is N = K 1 + b e − r t … ( 1 ) 1. The constant K is the carrying capacity. It is the limiting value of N . The point of inflection occurs at N = K / 2 . 2. The constant b is determined by b = K N ( 0 ) − 1 . 3. The r value is the intrinsic exponential growth rate. In the absence of limiting factors, growth would be exponential according to the formula N = N ( 0 ) e r t . The corresponding growth factor for this exponential function is a = e r , so we can find r from a using r = ln a . Calculation: Let N denote the sales per week after t weeks. Then, N ( 0 ) = 500 The limiting value of K is, K = 2500 copies per week . Calculate the value of constant b . b = K N ( 0 ) − 1 Substitute 2500 for K and 500 for N ( 0 ) in the above expression. b = 2500 500 − 1 = 5 − 1 = 4 Now the sales will grow by 10 % each week when no limiting factors are there

6th Edition

ISBN: 9781337801287

Author: Crauder

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 5.1, Problem 2TU

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A logistic model for newspaper circulation N as a function of time t in weeks.

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