From 1995 to 2003 the amount of mail m (in billions of pieces) handled by the u. s. postal service can be modeled by

Given that from 1995 to 2003, the amount of mail M (in billions of pieces) handled by the U.S. Postal Service can be modeled by



where t is the number of years since 1995. In which year was there about 204,000,000,000 pieces of mail handled?
Part a: 
Write a polynomial equation that can be used to answer the question.
The polynomial equation that can be used to answer the question is given by


Part b. 
List the possible whole-number solutions of the equation in part (a) that are less than or equal to 8.
The possible whole-number solutions of the equation in part (a) are the factors of 400.
Therefore, the possible whole-number solutions of the equation in part (a) that are less than or equal to 8 are 1, 2, 4, 5, 8

Part c:
Use synthetic division to determine which of the possible solutions in part (b) is an actual solution. Then answer the question in the problem statement.
Substituting t = 1 into the polynomial from part a, we have



Substituting t = 2 into the polynomial from part a, we have



Substituting t = 4 into the polynomial from part a, we have



Therefore, the year that there was about 204,000,000,000 pieces of mail handled is in 1995 + 4 = 1999

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