Thursday, June 22, 2017

June 2017: Common Core Algebra Regents, Part 4

The following are the questions and answers (and commentary) for part of the New York State Algebra Regents exam. If you have any questions or comments (or corrections), please add them in the Comments section.

My apologies for typos, particularly if they are in the questions, because then the answers are subject to change.

The answers to Part II can be found here.
The answers to Part III can be found here.

June 2017, Algebra I (Common Core), Part IV

36.Michael has $10 in his savings account. Option 1 will add $100 to his account each week. Option 2 will double the amount in his account at the end of each week.
Write a function in terms of x to model each option of saving.

Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike . Determine which option(s) will enable him to reach his goal. Justify your answer.

Option 1: f(x) = 100x + 10
Option 2: g(x) = 10(2)x

f(7) = 100(7) + 10 = 710
g(7) = 10(2)7 = 10(128) = 1280
Both options will enable him to reach his goal.

Your answer to the second part is dependent upon the function you wrote in the first part. If you made a mistake in the beginning, you need to carry that through to the end.

37. Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year.

Write a system of equations to model this situation, where x represents the number of years since 2010.

Graph this system of equations on the set of axes below.

Explain in detail what each coordinate of the point of intersection of these equations means in the context of this problem.

Swim: y = 10x + 5
Chorus: y = 5x + 35

In the graph (below), the coordinates of the point of intersection are (6, 65). The six means six years after 2010, or 2016. The 65 means that there will be 65 members on the swim team and in chorus.

End of Part IV

How did you do?
Comments, questions, corrections and concerns are all welcome.
Typos happen.

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