Rapid technological advancements have many many products obsolete. The rate of change of the market share of a new product (z) will be proportional to the market share of the new product and the market share of the old product at a given time (a) if the market is entirely described by the two products, and the market share of the new product is z, what is the market share of the old product? (b) set up the differential equation for dz dt Assume a growth constant of 4.5% (c) Find the equation for z, the market share of the new product, if it enters the market with 10% of the market share. hint: 1/ (1 − z)z = 1/ 1 − z + 1/ z
Rapid technological advancements have many many products obsolete. The rate of change of the market share of a new product (z) will be proportional to the market share of the new product and the market share of the old product at a given time (a) if the market is entirely described by the two products, and the market share of the new product is z, what is the market share of the old product? (b) set up the differential equation for dz dt Assume a growth constant of 4.5% (c) Find the equation for z, the market share of the new product, if it enters the market with 10% of the market share. hint: 1/ (1 − z)z = 1/ 1 − z + 1/ z
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Rapid technological advancements have many many products obsolete. The rate of change of the market share of a new product (z) will be proportional to the market share of the new product and the market share of the old product at a given time (a) if the market is entirely described by the two products, and the market share of the new product is z, what is the market share of the old product? (b) set up the differential equation for dz dt Assume a growth constant of 4.5%
(c) Find the equation for z, the market share of the new product, if it enters the market with 10% of the market share. hint: 1/ (1 − z)z = 1/ 1 − z + 1/ z
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