The local community-service funding organization in a certain county has classified the population into those who did not give the previous year, those who gave less than their "fair share," and those who met or exceeded their "fair share." Suppose the organization developed the following transition matrix for these groups. Find the steady-state vector for this county's contribution habits. 
Definitions:
Exact Simple Interest
Interest calculated precisely on the principal amount, without compounding, for a specific time period.
365-Day Year
A reference to a full calendar year consisting of 365 days, typically excluding leap years which have 366 days.
Exact Simple Interest Rate
The percentage of the principal amount (the initial sum of money borrowed or invested) that is paid as interest for a specified period, not accounting for compound interest.
365-Day Year
A conventional method used in finance to standardize the number of days in a year for interest calculation purposes.
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