August 2022 Algebra 2 Regents Part IV

This exam was adminstered in August 2022. These answers were not posted until they were unlocked on the NY Regents website or were posted elsewhere on the web.

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Algebra 2 August 2022

Part IV: A correct answer will receive 6 credits. Partial credit can be earned. One computational mistake will lose 1 point. A conceptual error will generally lose 2 points (unless the rubric states otherwise). It is sometimes possible to get 1 point for a correct answer with no correct work shown.


37. A technology company is comparing two plans for speeding up its technical support time. Plan A can be modeled by the function A(x) = 15.7(0.98)^x and plan B can be modeled by the function B(x) = 11(0.99)^x, where x is the number of customer service representatives employed by the company and A(x) and B(x) represent the average wait time, in minutes, of each customer.

Graph A(x) and B(x) in the interval 0 < x < 100 on the set of axes below.

To the nearest integer, solve the equation A(x) = B(x).

Determine, to the nearest minute, B(100) - A(100). Explain what this value represents in the given context.

Answer:

Start by putting the equations into your graphing calculators and copying down the points using the Table of Values. You were given a specific range, so DO NOT GRAPH PAST THAT RANGE. (You may notice the erasures on my graph below.)

Looking at the graph, to the nearest whole integer, A(x) = B(x) when x = 35, where the lines cross over. If your lines intersect at a different number, write that number down. You don't have to solve anything algebriacally.

B(100) - A(100) = 4.0 - 2.1 = 1.9 = 2 minutes. For 100 Customer service representatives, the average wait time is 2 minutes longer with plan B.

End of Exam

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