June 2023 Algebra 2 Regents Part IV

This exam was adminstered in June 2023.

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Algebra 2 June 2023

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. The volume of air in an average lung during breathing can be modeled by the graph below.

Using the graph, write an equation for N(t), in the form N(t) = A sin (Bt) + C.

That same lung, when engaged in exercise, has a volume that can be modeled by E(t) = 2000 sin(πt) + 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) = E(t)?

Answer:

A is the height of the graph from the midline, which is 400. B is the period which is 2π/5 because it takes 5 seconds before 2 pi is graphed. C is the midline, which is 2400. Since the graph starts at the midline, it is a sine function, not a cosine function.

The equation will be T = (400 - 75)e^-.0735t + 75.

For the second part, look at the graph below.

In a 5-second interval, N(t) = E(t) four times.

End of Exam

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