A poll shows that half of the consumers who use brand a switched to brand b the following year, while the other half stayed with brand a. 9/10 of the brand b users stayed with brand b the following year while the rest switched. In the long term, what fraction of the time will a user spend using each of the two brands?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 71E
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A poll shows that half of the consumers who use brand a switched to brand b the following year, while the other half stayed with brand a. 9/10 of the brand b users stayed with brand b the following year while the rest switched. In the long term, what fraction of the time will a user spend using each of the two brands? (Enter your answers as fractions)

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